Exhibit 99.1

IMMEDIATE RELEASE

Graham Corporation Reports

Fiscal 2016 Fourth Quarter and Full Year Results

BATAVIA, NY, May 25, 2016 – 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 results for its fourth quarter and fiscal year ended March 31, 2016 (“fiscal 2016”).

Net sales in the fourth quarter of fiscal 2016 were $22.3 million, compared with net sales of $37.5 million in the fourth quarter of the fiscal year ended March 31, 2015 (“fiscal 2015”). Similar to earlier fiscal 2016 quarters, fourth quarter sales were impacted by weak market conditions. Net income in the fourth quarter was $0.5 million, or $0.05 per diluted share. The prior year’s fourth quarter had net income of $4.2 million, or $0.41 per diluted share.

Net sales for the full-year fiscal 2016 were $90.0 million, a decrease of 33% from $135.2 million in fiscal 2015. Fiscal 2016 net income was $6.1 million, or $0.61 per diluted share, compared with net income of $14.7 million, or $1.45 per diluted share, in fiscal 2015.

James R. Lines, Graham’s President and Chief Executive Officer, commented, “The dramatic decline in crude oil prices over the past 12 to 18 months presented significant challenges to our business. The impact on Graham is evidenced by year-over-year revenue and order declines from last year’s record levels, as well as lower earnings. Despite this difficult operating environment, I believe that Graham today is a stronger, more diverse and better performing company than in past downturns. This is due, in large part, to actions we have taken both to change how we operate in the cyclical markets that we serve and to grow our revenue opportunities in more non-cyclical markets. These actions enabled us, in fiscal 2016, to maintain profitability and strong cash flows from operations, while allowing us to remain committed to our long-term growth strategies.”

Fourth Quarter Sales Summary

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

Sales to the power market were up 49%, to $5.2 million, while sales to all other markets were down compared with the prior year fourth quarter. Graham believes that the improvement in the power market sales demonstrates the effectiveness of its diversification strategy. From a geographic perspective, sales to most markets were down compared with the prior-year fourth quarter. Sales to the U.S. market were $13.4 million, or 60% of consolidated fourth quarter sales in fiscal 2016. Sales to markets outside of the U.S. accounted for $8.9 million, or 40%.

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Fluctuations in Graham’s sales among geographic locations and industries 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 2016 Operating Performance

Gross profit in the fourth quarter was $4.6 million, or 20% of sales, compared with $12.8 million, or 34% of sales, in the same period of the prior fiscal year. Fourth quarter gross profit and margin were impacted by lower revenue and production volume causing under-absorption of overhead, personnel investments for commercial nuclear and naval strategies, and the impact of lower margin orders from backlog.

Selling, general and administrative (“SG&A”) expenses were $3.9 million in the fourth quarter, down 20% from $4.9 million in the same prior-year period. This decrease was principally due to lower variable expenses, including compensation, as well as cost reductions stemming from the restructuring activity that occurred at the end of fiscal 2015. SG&A as a percent of sales was 18% in the fourth quarter of fiscal 2016 compared with 13% in the same prior-year period.

The fourth quarter of the prior year included a $1.7 million restructuring charge, primarily for severance costs related largely to a voluntary early retirement program.

Fourth quarter net income was $0.5 million, compared with net income of $4.2 million in the prior-year fourth quarter. Consolidated net income before interest expense and income, income taxes, depreciation and amortization and a nonrecurring restructuring charge (“Adjusted EBITDA”) was $1.2 million in the fourth quarter, compared with $8.4 million in the same prior-year period. Adjusted EBITDA margin, which refers to Adjusted EBITDA as a percentage of sales, in the fourth quarter was 5% compared with 23% in the prior-year period. Graham believes that when used in conjunction with measures prepared in accordance with U.S. generally accepted accounting principles (“GAAP”), Adjusted EBITDA and Adjusted EBITDA margin, which are non-GAAP measures, help 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 and Adjusted EBITDA margin as well as a reconciliation of net income to Adjusted EBITDA.

Graham’s effective tax rate for the fourth quarter of fiscal 2016 was 26% compared with 33% for the same prior-year period.

Full Year Fiscal 2016 Review

Net sales of $90.0 million in fiscal 2016 reflected weak fundamentals in the refining and chemical industries globally. International sales were $33.0 million and represented 37% of total sales compared with $48.8 million, or 36% of sales, in the prior-year period. Sales to the U.S. were $57.0 million, or 63% of net sales, compared with $86.4 million, or 64% of net sales, for fiscal 2015.

Gross profit was down $18.5 million to $23.3 million, compared with the prior-year period, primarily as a result of lower volume and also due to personnel investments to support the Company’s commercial nuclear and naval strategies. Gross margin was 26% for fiscal 2016 compared with 31% in the prior year. SG&A was $16.6 million, down 11%, or $1.9 million, principally due to lower variable expenses, including compensation, as well as cost reductions resulting from the restructuring activity in fiscal 2015. As a percent of sales, SG&A was 18% compared with 14% in the prior year, reflecting lower sales volume.

As noted above, the prior year included a $1.7 million restructuring charge primarily for severance costs related largely to a voluntary early retirement program.

Other income was $1.8 million in fiscal 2016 due to cancellation charges received in the third quarter.

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Fiscal 2016 net income was $6.1 million, compared with net income of $14.7 million in the prior year. Adjusted EBITDA was $10.9 million, compared with $25.6 million in the prior year. As a percent of sales, Adjusted EBITDA was 12%, compared with 19% in the prior year, reflecting the impact of volume and under absorbed overhead. 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.

Graham’s effective tax rate for fiscal 2016 was 30%, compared with 32% for fiscal 2015. Taxes for fiscal 2016 were favorably impacted by the U.S. government’s retroactive reinstatement of the federal research and development tax credit during the Company’s fiscal third quarter.

Strong Cash Flows Provide Increased Returns to Shareholders as well as Reserves for Growth

Cash, cash equivalents and investments at March 31, 2016 were $65.1 million, reflecting a $4.8 million increase compared with ending balances at March 31, 2015.

Cash provided by operations in fiscal 2016 was $18.8 million, compared with $6.3 million in fiscal 2015. The significant increase was due to strong customer collections, partially offset by lower net income and decreases in certain current liabilities.

Capital expenditures were $1.2 million in fiscal 2016, compared with $5.3 million in the prior year. The majority of the prior year’s spending was for capacity expansion of the Company’s Batavia, New York facility, including that to support growth in U.S. Navy revenue. The Company expects capital expenditures for fiscal 2017 to be between $2.0 million and $2.5 million, primarily for equipment upgrades and productivity enhancements.

Graham had neither borrowings under its credit facility, nor any long-term debt outstanding, at March 31, 2016.

Jeffrey Glajch, Graham’s Chief Financial Officer, commented, “We are pleased that we were able to return $12.7 million to shareholders during fiscal 2016 and still grow our cash and investment balances by $4.8 million. Our cash returns to shareholders included $3.3 million in dividends and $9.4 million in share repurchases made pursuant to our previously announced share repurchase program. We believe that the strength of our operations, regardless of the point in the economic cycle, together with our cash reserves, will continue to support our growth plans, both organically and through acquisition.”

Backlog Demonstrates Effects of Diversification Strategy

Orders during the fourth quarter of fiscal 2016 were $17.1 million, net of a $4.9 million cancellation from backlog, down from $47.4 million in the prior-year fourth quarter which included significant orders from the U.S. Navy. Gross orders were $22.0 million in the fiscal 2016 fourth quarter. Orders from the power and refining markets increased $5.5 million and $2.4 million, respectively. Chemical/petrochemical market orders were down $6.3 million compared with the prior-year quarter. Other commercial, industrial and defense orders were down $31.9 million. There were two orders for the refining industry on hold as of March 31, 2016, valued at $6.4 million.

Orders from U.S. customers were $19.7 million in the fiscal 2016 fourth quarter. Orders from international markets, net of a $4.9 million cancellation, were negative $2.6 million.

Graham expects that the balance between domestic and international orders will continue to be variable between quarters, but that in the long run orders will be relatively balanced between these geographic markets.

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The Company’s backlog was $108.0 million at March 31, 2016, compared with $113.2 million at December 31, 2015, and $113.8 million at March 31, 2015. Approximately 21% of backlog was for refinery projects, 11% was for chemical and petrochemical projects and 17% was for power projects, including nuclear. Approximately 47% of backlog was for U.S. Navy projects and 4% was for other industrial or commercial applications.

Approximately 45% to 55% of orders currently in backlog are expected to be converted to sales within the next 12 months, approximately 10% to 20% are expected to be converted between the next 12 to 24 months, and approximately 35% to 45% are expected to be converted beyond 24 months.

Fiscal 2017 Guidance Anticipates Increased Sales to the Power Market

The Company expects fiscal 2017 revenue to be between $80 million and $95 million. Gross margin for fiscal 2017 is expected to be between 24% and 26%, reflecting continued pricing pressure, underutilization of production facilities, and personnel investments associated with naval and commercial nuclear diversification strategies. SG&A expense is estimated to be between $17.5 million and $18.5 million in fiscal 2017. Graham is projecting its fiscal 2017 effective tax rate to be between 32% and 33%.

Mr. Lines concluded, “While our refining and chemical industry markets continue to exhibit considerable uncertainty, we will continue to aggressively pursue new orders and defend our leading market position. To reach the upper end of our revenue expectations, we require favorable conditions within our more diverse markets and improvement in the energy markets. We expect to grow revenue in the utility nuclear power market, as our initiatives to gain market share have started to materialize. Looking further out, we expect revenue from the U.S. Navy will meaningfully expand in fiscal 2018. As we explore inorganic growth opportunities, we are encouraged by the receptiveness of management teams at target companies to engage in discussions regarding potential acquisition by Graham.”

Webcast and Conference Call

Graham 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 the fiscal 2016 fourth quarter and full year, as well as its strategy and outlook. The review will be accompanied by a slide presentation which will be made available immediately prior to the conference call on Graham’s website 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 under the heading “Investor Relations.”

A telephonic replay will be available from approximately 2:00 p.m. Eastern Time on the day of the call through Wednesday, June 1, 2016. To listen to the archived call, dial (858) 384-5517, and enter conference ID number 13635236. A transcript of the call will be placed on Graham’s website, once available.

ABOUT GRAHAM CORPORATION

Graham is a global business that designs, manufactures and sells critical equipment for the energy, defense and chemical/petrochemical industries. Energy markets include oil refining, cogeneration, nuclear and alternative power. For the defense industry, the Company’s equipment is used in nuclear propulsion power systems for the U.S. Navy. Graham’s global brand is built upon world-renowned engineering expertise in vacuum and heat transfer technology, responsive and flexible service and unsurpassed quality. Graham designs and manufactures custom-engineered ejectors, vacuum pumping systems, surface condensers and vacuum systems. Graham is also a leading nuclear code accredited fabrication and specialty machining company. Graham supplies components used inside reactor vessels and outside containment vessels of nuclear power facilities. Graham’s equipment can also be found in other diverse applications such as metal refining, pulp and paper processing, water heating, refrigeration, desalination, food processing, pharmaceutical, heating, ventilating and air conditioning. Graham’s reach

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spans the globe and 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.

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,” “aim,” “pursuit,” 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 EBITDA Reconciliation—Unaudited

(Amounts in thousands)

Non-GAAP Financial Measures:

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 margin is Adjusted EBITDA divided by sales. Adjusted EBITDA and Adjusted EBITDA margin are not measures 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 and Adjusted EBITDA margin are important for investors and other readers of Graham’s financial statements, as they are used as analytical indicators by Graham’s management to better understand operating performance. Graham’s credit facility also contains ratios based on EBITDA. Because Adjusted EBITDA and Adjusted EBITDA margin are non-GAAP measures and are thus susceptible to varying calculations, Adjusted EBITDA and Adjusted EBITDA margin, 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

SALES BY INDUSTRY FY 2016

($ in millions)

SALES BY INDUSTRY FY 2015

($ in millions)

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Graham Corporation

Additional Information—Unaudited

(Continued)

SALES BY REGION FY 2016

($ in millions)

SALES BY REGION FY 2015

($ in millions)

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