Exhibit 99.1

Graham Corporation 20 Florence Avenue Batavia, NY 14020

IMMEDIATE RELEASE

Graham Corporation Reports Record Fiscal 2015 Sales

BATAVIA, NY, May 29, 2015 – Graham Corporation (NYSE: GHM), a global business that designs, manufactures and sells critical equipment for the oil refining, petrochemical, power and defense industries, today reported its financial and operating results for its fourth quarter and full year ended March 31, 2015 (“fiscal 2015”).

Net sales in the fourth quarter of fiscal 2015 were $37.5 million, up 44% from net sales of $26.1 million in the fourth quarter of the fiscal year ended March 31, 2014 (“fiscal 2014”). Net income for the reported quarter was $4.2 million, or $0.41 per diluted share, compared with $2.3 million, or $0.23 per diluted share, in the prior year’s fourth quarter. Excluding a $1.1 million, net of tax, nonrecurring restructuring charge recorded in the fiscal 2015 fourth quarter, adjusted net income, a non-GAAP number, was $5.3 million or $0.53 per diluted share. Adjusted net income as a percent of sales was 14% in the fourth quarter. Graham believes that, when used in conjunction with measures prepared in accordance with U.S. generally accepted accounting principles (“GAAP”), adjusted net income helps in the understanding of its operating performance. See the attached tables for additional important disclosures regarding Graham’s use of adjusted net income as well as a reconciliation of GAAP net income to non-GAAP adjusted net income.

Net sales for the full-year fiscal 2015 were a record $135.2 million, up 32% from $102.2 million in fiscal 2014. Fiscal 2015 net income was $14.7 million, or $1.45 per diluted share, up from $10.1 million, or $1.00 per diluted share, in fiscal 2014. Excluding the fourth quarter’s nonrecurring restructuring charge, adjusted net income was $15.9 million, or $1.57 per diluted share, in fiscal 2015. Accordingly, adjusted net income per diluted share grew 57% over the prior year. Adjusted net income as a percent of sales was 12% for fiscal 2015.

James R. Lines, Graham’s President and Chief Executive Officer, commented, “Fiscal 2015 was an outstanding year. We set new records for sales, orders and year-end backlog. We realized operational leverage on the investments made over the prior three years, as we executed our strategy to take Graham to a new level. We believe these results demonstrate our ability to concurrently deliver remarkable financial performance and provide exceptional customer value.”

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Refining and Chemical/Petrochemical Sales Drive Fourth Quarter Fiscal 2015 Growth

(See accompanying tables for a breakdown of sales by industry and region)

When compared with the same prior-year period, refining and chemical/petrochemical industry sales in the fourth quarter increased $6.0 million and $3.0 million, or 103% and 28%, respectively. Sales to the Company’s other commercial and industrial markets, including defense, increased by $3.8 million. Sales to the power industry, which includes nuclear, decreased $1.4 million.

By geographic market, sales in the fourth quarter increased $3.7 million to the U.S. market and $3.5 million to the Middle East market. Sales to the Asia market and the Company’s category of Other geographic markets were up by $2.5 million and $1.7 million, respectively. International sales represented 36% of fiscal 2015’s fourth quarter sales.

Fluctuations in Graham’s sales among industries and geographic locations can vary measurably from quarter-to-quarter based on the timing and magnitude of projects. Graham does not believe that such quarter-to-quarter fluctuations are indicative of business trends, which it believes are more apparent on a trailing twelve month basis.

Fourth Quarter Fiscal 2015 Operating Performance

Gross profit for the reported quarter was $12.8 million, or 34% of sales, compared with $7.4 million, or 28% of sales, in the same period of the prior fiscal year. Gross profit and margin were favorably impacted by sales volume, however the result was muted by lower pricing for certain orders and higher levels of subcontracting in the quarter.

Selling, general and administrative (“SG&A”) expenses were $4.9 million in the fourth quarter compared with $4.2 million in the same period last year. As a percent of sales, SG&A was 13% compared with 16% in the same prior-year quarter.

The Company incurred a pre-tax restructuring charge of $1.7 million for severance costs related to a voluntary early retirement program offered to employees during the fourth quarter of fiscal 2015. As a result of the restructuring, which is expected to be completed in the second quarter, the global workforce headcount will be reduced by approximately 10%. Graham intends to retain the infrastructure and skilled employee base that it believes will enable the Company to seize market opportunities upon the commencement of the next recovery in its refining and petrochemical markets.

Operating profit in the fourth quarter of fiscal 2015 was $6.1 million, or 16% of sales, compared with $3.2 million, or 12% of sales, in the fourth quarter of fiscal 2014. The improvement was driven primarily by sales volume, which was partially offset by the nonrecurring restructuring charge.

Adjusted earnings before interest, taxes, depreciation and amortization (“Adjusted EBITDA”) in the current quarter was $8.4 million, or 23% of sales, compared with $3.7 million, or 14% of sales, in the same period of the prior fiscal year. Graham believes that, when used in conjunction with measures prepared in accordance with “GAAP”, Adjusted EBITDA, which is a non-GAAP measure, helps in the understanding of its operating performance. Graham’s credit facility also contains ratios based on EBITDA. See the attached tables for additional important disclosures regarding Graham’s use of Adjusted EBITDA as well as a reconciliation of net income to Adjusted EBITDA.

Full Year Fiscal 2015 Review

Sales were $135.2 million, of which 64% were to the U.S. market. U.S. sales increased $22.6 million, or 35%, to $86.4 million compared with the prior year, driven principally by sales to the chemical/petrochemical industry along with increased sales to other commercial and industrial, and refining industries. International sales of $48.8 million, which were 36% of total sales, increased 27%, or $10.4 million, when compared with fiscal 2014.

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Gross profit was $41.8 million compared with $31.8 million in the prior year. As a percent of sales, gross margin was unchanged from the prior year at 31%. SG&A expenses were $18.5 million, up $1.3 million. As a percent of sales, SG&A was 14% compared with 17% in fiscal 2014. As noted previously, there was a $1.7 million pre-tax, nonrecurring restructuring charge in fiscal 2015. Operating profit for fiscal 2015 was $21.6 million, or 16% of sales, compared with $14.6 million, or 14% of sales, in fiscal 2014.

Adjusted EBITDA in fiscal 2015 was $25.6 million, or 19% of sales, compared with $16.8 million, or 17% of sales, in fiscal 2014.

Strong Balance Sheet with No Debt

Cash, cash equivalents and investments at March 31, 2015, were $60.3 million, compared with $62.5 million at December 31, 2014 and $61.1 million at March 31, 2014.

Cash provided by operations in fiscal 2015 was $6.3 million, compared with $15.2 million in fiscal 2014, lower primarily due to timing of collections on accounts receivable and unbilled revenue.

Capital expenditures were $5.3 million in fiscal 2015, consistent with the prior fiscal year. Approximately 65% of the capital expenditures in both years supported the expansion of Graham’s Batavia, New York manufacturing facility, which began in the second half of fiscal 2014 and was completed in the first half of fiscal 2015. Capital expenditures in fiscal 2016 are expected to be between $2 million and $2.5 million, primarily for equipment upgrades and productivity.

Graham had neither borrowings under its credit facility, nor any long-term debt outstanding at March 31, 2015.

As of March 31, 2015, Graham had not made any stock repurchases under the previously-announced $18 million stock repurchase program.

Fourth Quarter and Fiscal 2015 Orders and Backlog

Orders during the fourth quarter of fiscal 2015 were $47.4 million, net of the impact of $5.9 million of orders cancelled and removed from backlog in the quarter, up from $23.5 million in the same quarter last year, and up sequentially from $22.6 million in the third quarter of fiscal 2015. Approximately 25% of fourth quarter orders, net of cancellations, came from the refining, chemical/petrochemical and power markets.

For the full year, orders increased 7% to a record level of $136.5 million, compared with $128.2 million in the prior fiscal year. Orders received during fiscal 2015 were 67% from the U.S. market, benefiting from the fourth quarter U.S. Navy order. Orders from the other commercial and industrial category, which includes defense, and oil refining markets increased 77% and 34%, respectively. Orders from the chemical/petrochemical market were 33% lower, impacted by lower domestic demand.

Graham’s backlog was a year-end record level at $113.8 million, up 2% from $112.1 million at March 31, 2014. Backlog at the end of the year included approximately 24% for refinery projects, 15% for chemical/petrochemical projects, 9% for power projects, including nuclear energy, 48% for U.S. Navy projects and 4% for all other industries served by Graham. At March 31, 2015, there were no projects on hold; however, approximately $10 million of projects have been delayed by the Company’s customers until fiscal 2017. Approximately 45% to 50% of orders currently in backlog are expected to be converted to sales within one year and 40% to 45% beyond two years.

Fiscal 2016 Guidance; Long-Term Outlook Remains Intact

For fiscal 2016, Graham expects sales to be in the range of $95 million to $105 million. Gross margin for fiscal 2016 is expected to be between 26% and 28%, resulting from anticipated lower production facility utilization and increased pricing pressure. SG&A expense as a percent of sales

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is expected to be between 17% and 18% for fiscal 2016. Graham expects its fiscal 2016 full year effective tax rate to be approximately 32% to 33%.

Mr. Lines noted, “We believe the long-term outlook for the energy markets remains strong, driven by expected continued expansion in the global consumption of crude oil and petrochemicals, notwithstanding the challenges we face in the current market. Additionally, we expect that our diversification strategy to grow our predictable base business, which includes the U.S. Navy, the nuclear power market and short-cycle and aftermarket products and services, will help to dampen the impact on our business of the cyclicality in the refining and petrochemical industries. We believe the success of this diversification strategy is reflected in our record year-end backlog, of which approximately 55% is from markets or customers not served by the Company just five years ago.”

He concluded, “Our near-term objective to double organic revenue and drive our EBITDA margins to the low-to-mid 20% range remains intact, with timing subject to market conditions. We intend to continue to leverage our assets to capture market share, expand our predictable base business, and strengthen our revenue opportunities in support of our commitment to generate shareholder value.”

Webcast and Conference Call

Graham’s management will host a conference call and live webcast today at 11:00 a.m. eastern time to review Graham’s financial condition and operating results for its fourth quarter and full year fiscal 2015, as well as its strategy and outlook. The review will be accompanied by a slide presentation which will be made available prior to the conference call on Graham’s website located at www.graham-mfg.com under the heading “Investor Relations.” A question-and-answer session will follow the formal presentation.

Graham’s conference call can be accessed by calling (201) 689-8560. Alternatively, the webcast can be monitored on Graham’s website at www.graham-mfg.com.

A telephonic replay will be available from approximately 2:00 p.m. Eastern Time on the day of the call through Friday, June 5, 2015. To listen to the archived replay of the call, dial (858) 384-5517, and enter replay pin number 13606824. A transcript of the call will be placed on Graham’s website, once available.

ABOUT GRAHAM CORPORATION

With world-renowned engineering expertise in vacuum and heat transfer technology, Graham Corporation is a global designer, manufacturer and supplier of custom-engineered ejectors, pumps, condensers, vacuum systems and heat exchangers. For nearly 80 years, Graham has built a reputation for top quality, reliable products and high-standards of customer service. Sold either as components or complete system solutions, Graham’s equipment is found in the energy industry, including oil and gas refining and nuclear and other power generation, the defense industry, primarily for naval nuclear propulsion systems, as well as chemical/petrochemical and other process industries. In addition, Graham’s equipment can be found in diverse applications, such as metal refining, pulp and paper processing, water heating, refrigeration, desalination, food processing, pharmaceutical, heating, ventilating and air conditioning, and in nuclear power installations, both inside the reactor vessel and outside the containment vessel.

Graham Corporation’s subsidiary Energy Steel & Supply Co. is a leading code fabrication and specialty machining company dedicated exclusively to the nuclear power industry.

Graham Corporation’s reach spans the globe. Its equipment is installed in facilities from North and South America to Europe, Asia, Africa and the Middle East. Graham routinely posts news and other important information on its website, www.graham-mfg.com, where additional comprehensive information on Graham Corporation and its subsidiaries can be found.

Safe Harbor Regarding Forward Looking Statements

This news release contains forward-looking statements within the meaning of Section 27A of the Securities Act of 1933, as amended, and Section 21E of the Securities Exchange Act of 1934, as amended.

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Forward-looking statements are subject to risks, uncertainties and assumptions and are identified by words such as “expects,” “estimates,” “confidence,” “projects,” “typically,” :outlook,” “anticipates,” “believes,” “appears,” “could,” “opportunities,” seeking,” “plans,” and other similar words. All statements addressing operating performance, events, or developments that Graham Corporation expects or anticipates will occur in the future, including but not limited to, expected expansion and growth opportunities within the domestic and international markets, anticipated revenue, the timing of conversion of backlog to sales, market presence, profit margins, tax rates, foreign sales operations, its ability to improve cost competitiveness, customer preferences, changes in market conditions in the industries in which it operates, changes in commodities prices, the effect on its business of volatility in commodities prices, changes in general economic conditions and customer behavior, forecasts regarding the timing and scope of the economic recovery in its markets, its acquisition and growth strategy and the expected performance of Energy Steel & Supply Co, are forward-looking statements. Because they are forward-looking, they should be evaluated in light of important risk factors and uncertainties. These risk factors and uncertainties are more fully described in Graham Corporation’s most recent Annual Report filed with the Securities and Exchange Commission, included under the heading entitled “Risk Factors.”

Should one or more of these risks or uncertainties materialize, or should any of Graham Corporation’s underlying assumptions prove incorrect, actual results may vary materially from those currently anticipated. In addition, undue reliance should not be placed on Graham Corporation’s forward-looking statements. Except as required by law, Graham Corporation disclaims any obligation to update or publicly announce any revisions to any of the forward-looking statements contained in this news release.

FINANCIAL TABLES FOLLOW.

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Graham Corporation

Consolidated Statements of Operations

(Amounts in thousands, except per share data)

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Graham Corporation

Consolidated Balance Sheets

(Amounts in thousands, except per share data)

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Graham Corporation

Consolidated Statements of Cash Flows

(Amounts in thousands)

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Graham Corporation

Adjusted Net Income Reconciliation—Unaudited

(Amounts in thousands, except per share data)

Non-GAAP Financial Measure:

Adjusted net income is GAAP net income excluding a nonrecurring restructuring charge. Adjusted net income is not a measure determined in accordance with generally accepted accounting principles in the United States, commonly known as GAAP. Nevertheless, Graham believes that providing non-GAAP information such as Adjusted net income is important for investors and other readers of Graham’s financial statements, as it is used as an analytical indicator by Graham’s management to better understand operating performance. Because Adjusted net income is a non-GAAP measure and is thus susceptible to varying calculations, Adjusted net income, as presented, may not be directly comparable to other similarly titled measures used by other companies.

Graham Corporation

Adjusted EBITDA Reconciliation—Unaudited

(Amounts in thousands)

Non-GAAP Financial Measure:

Adjusted EBITDA is defined as consolidated net income before interest expense and income, income taxes, depreciation and amortization and a nonrecurring restructuring charge. Adjusted EBITDA is not a measure determined in accordance with generally accepted accounting principles in the United States, commonly known as GAAP. Nevertheless, Graham believes that providing non-GAAP information such as Adjusted EBITDA is important for investors and other readers of Graham’s financial statements, as it is used as an analytical indicator by Graham’s management to better understand operating performance. Graham’s credit facility also contains ratios based on EBITDA. Because Adjusted EBITDA is a non-GAAP measure and is thus susceptible to varying calculations, Adjusted EBITDA, as presented, may not be directly comparable to other similarly titled measures used by other companies.

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Graham Corporation

Additional Information—Unaudited

ORDER & BACKLOG TREND

($ in millions)

SALES BY INDUSTRY FY 2015

($ in millions)

SALES BY INDUSTRY FY 2014

($ in millions)

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Graham Corporation

Additional Information—Unaudited

(Continued)

SALES BY REGION FY 2015

($ in millions)

SALES BY REGION FY 2014

($ in millions)

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