Exhibit 99.1

Graham Corporation 20 Florence Avenue Batavia, NY 14020

IMMEDIATE RELEASE

Graham Corporation Reports 45% Revenue Growth in Fiscal 2015 Second Quarter

BATAVIA, NY, October 29, 2014 – Graham Corporation (NYSE MKT: GHM), a global business that designs, manufactures and sells critical equipment for the oil refining, petrochemical and power industries, including the supply of components and raw materials to nuclear energy facilities, today reported its financial results for its second quarter ended September 30, 2014. Graham’s current fiscal year (“fiscal 2015”) ends March 31, 2015.

Net sales in the second quarter of fiscal 2015 were $35.6 million, up 45% from net sales of $24.5 million in the second quarter of the fiscal year ended March 31, 2014 (“fiscal 2014”). Second quarter fiscal 2015 sales were driven by domestic petrochemical orders received during the first half of fiscal 2014 as well as from higher sales to oil refining markets in South America and the Middle East. Net income was $4.2 million, or $0.41 per diluted share, which represents an increase of 62% over the prior year’s quarter.

James R. Lines, Graham’s President and Chief Executive Officer, commented, “We had strong performance in the quarter with sales and earnings growth in line with our expectations, as significant petrochemical projects in our backlog moved through production. We achieved a record level of quarterly sales because of investments we have made over the last several years to increase our throughput in both engineering and production. Of note, the ongoing strength of both our backlog and bidding pipeline give us confidence in our outlook for fiscal 2015 and beyond.”

U.S. Petrochemical Market Drives Strong Sales in Second Quarter

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

Sales to the U.S. market were up $7.8 million, or 55%, to $21.9 million. Sales to markets outside of the U.S. accounted for an aggregate increase of $3.3 million, or 32%, further contributing to the $11.1 million increase in net sales over the prior year’s quarter.

Petrochemical sales more than tripled in the second quarter of fiscal 2015 to $12.9 million, compared with the same prior-year period, on higher demand for Graham’s engineered-to-order products from the North American petrochemical and chemical industries.

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.

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Graham Corporation Reports 45% Revenue Growth in Fiscal 2015 Second Quarter

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Second Quarter Fiscal 2015 Operating Performance

Gross profit was $11.0 million, or 30.9% of sales, compared with $8.3 million, or 33.8% of sales, in the same period of the prior fiscal year. Fiscal 2015’s second quarter gross profit dollars increased on higher volume and gross margin declined on project mix. On a sequential basis compared with the first quarter of fiscal 2015, gross margin expanded 310 basis points, demonstrating strong leverage on 25% higher revenue.

Jeffrey Glajch, Graham’s Chief Financial Officer, commented, “We believe that our sequential gross margin improvement validates the strength of our business model and the leverage that we can generate on volume growth with comparable sales mix. Our fiscal 2015 second quarter sales mix was more heavily weighted toward surface condensers for the petrochemical market. Last year’s second quarter had the benefit of more revenue from ejector systems and spares required primarily by the oil refining industry, which generally have higher gross profit margins.”

Selling, general and administrative (“SG&A”) expenses were $4.8 million, up 7% from $4.4 million in the same prior-year period. SG&A as a percent of sales was 13.4% in the second quarter of fiscal 2015 compared with 18.2% in the same prior-year period. The decline as a percent of sales was due to the lower variable cost of sales for the specific projects shipped in the quarter combined with the fixed nature of the Company’s supporting infrastructure.

Operating profit increased 62% to $6.2 million, or 17.5% of sales, compared with $3.8 million, or 15.7% of sales, in the second quarter of fiscal 2014. The 180 basis point improvement was due to the strong operating leverage inherent in the Company’s operations. On a sequential basis, operating margin expanded 490 basis points.

Earnings before interest, taxes, depreciation, and amortization (“EBITDA”) were $6.8 million, compared with $4.4 million in the prior-year period. EBITDA margin improved 130 basis points to 19.2% of sales. Graham believes that when used in conjunction with measures prepared in accordance with U.S. generally accepted accounting principles (“GAAP”), 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 EBITDA as well as a reconciliation of net income to EBITDA.

Graham’s effective tax rate for the second quarter of fiscal 2015 was 33%, consistent with the prior-year period.

First Half Fiscal 2015 Review

Net sales were $64.1 million, up 21% from $52.7 million in the first six months of fiscal 2014. International sales were $20.0 million and represented 31% of total sales compared with $23.7 million or 45% of sales, in the prior-year period. Sales to the U.S. increased $15.0 million, or 52%, to $44.1 million.

Gross profit was $18.9 million, up $0.6 million when compared with $18.3 million in gross profit in the prior-year period, primarily on higher volume. Gross margin was 29.5% for the fiscal 2015 six-month period compared with 34.7% in the first half of fiscal 2014, due to the change in product mix. SG&A expenses in the fiscal 2015 first half were $9.1 million, up 3% or $0.2 million. As a percent of sales, SG&A was 14.2% in the first half of fiscal 2015 compared with 16.8% in the same prior-year period.

EBITDA was $11.0 million compared with $10.6 million the prior-year period. As a percent of sales, EBITDA was 17.1% compared with 20.0% last year, reflecting the changes in product mix. See the attached tables for additional important disclosures regarding Graham’s use of EBITDA as well as a reconciliation of net income to EBITDA.

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Net income for the first half of fiscal 2015 was $6.6 million, or $0.65 per diluted share, improved over net income of $6.4 million, or $0.63 per diluted share, in the first six months of fiscal 2014.

Strong Balance Sheet Supports Growth Initiatives

Cash, cash equivalents and investments at September 30, 2014 increased $3.7 million to $64.8 million, compared with ending balances at March 31, 2014.

Cash provided by operations in the second quarter and first half of fiscal 2015 were $5.3 million and $8.5 million, respectively, a strong improvement compared with $2.3 million and $4.3 million in the second quarter and first half of fiscal 2014, respectively.

Capital expenditures were $4.1 million in the first half of fiscal 2015, up from $0.9 million in the first half of fiscal 2014. The Company continues to expect capital expenditures for fiscal 2015 to be approximately $5.5 million to $6 million. Approximately 60% of the annual capital spending is for the Company’s Batavia, New York facility expansion, which was completed during the second quarter of fiscal 2015.

Graham had neither borrowings under its credit facility, nor any long-term debt outstanding, at September 30, 2014.

Continued Record Backlog

Orders during the second quarter of fiscal 2015 were $35.4 million, down $13.0 million from $48.4 million in the second quarter of fiscal 2014. The change in order level reflects expected quarterly variability based on customer project timing, in this case primarily from the chemical/petrochemical industry and from other commercial and industrial applications, including the U.S. Navy. When compared with the trailing first quarter of fiscal 2015, orders increased 14%, or $4.3 million.

Orders from U.S. customers represented 47%, or $16.7 million, of total orders received during the second quarter of fiscal 2015, while orders from international markets accounted for $18.7 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.

The Company’s backlog remained at a record level of $114.8 million at September 30, 2014, consistent with the level at June 30, 2014 and up from $112.1 million at March 31, 2014. Approximately 38% of backlog was for refinery projects, 21% was for chemical and petrochemical projects and 13% was for power projects, including nuclear. Approximately 21% of backlog was for U.S. Navy projects and 7% was for other industrial or commercial applications. As of September 30, 2014, $7.8 million of backlog was on hold pending the end-user’s analysis of final project design. The order was awarded and put on hold during the fiscal 2015 second quarter. Graham expects that the hold will be released within fiscal 2015 and anticipates shipment 24 to 36 months subsequent to its release.

Approximately 70% to 75% of orders currently in backlog are expected to be converted to sales within the next 12 months, approximately 15% to 20% are expected to be converted within the next 12 to 24 months, and approximately 5% to 10% are expected to be converted beyond 24 months.

Mr. Lines noted, “We continue to benefit from solid progress in our core refining and petrochemical markets. Importantly, we are successfully capturing greater market share in these industries, enabled by our increased capacity. Concurrently, we are working on building a stronger, more predictable base business with our U.S. Navy, nuclear and short cycle opportunities. We expect this less cyclical base of business to become a much larger contributor to overall revenue over time.”

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Tightened Revenue Guidance to Upper End of Range With Visibility on Shipment Timing

The Company has tightened its fiscal 2015 revenue expectations to be between $125 million and $130 million, the upper end of its previously provided $120 million to $130 million range. This reflects 22% to 27% growth over fiscal 2014. Gross margin guidance for fiscal 2015 has been refined to a range of 30% to 31% from 30% to 32%, reflecting the project mix in backlog. SG&A expense guidance has also been tightened to between 15% and 15.5% of sales, which is above the rate for the first half of the year based on higher sales commissions anticipated in the second half of the year. Graham expects its fiscal 2015 full year tax rate to be approximately 33% to 34%, which remains unchanged from prior guidance.

Mr. Lines concluded, “We believe that our strategy of investing in our facilities, equipment, people and processes has enabled us to deliver strong growth and solid earnings power. We intend to continue to drive this growth by taking greater market share, leveraging our expanding installed base around the world and providing value to our customers through our engineering expertise and ability to deliver high quality, reliable, engineered-to-order solutions.”

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 its second quarter and first half of fiscal 2015, 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.

To listen to the archived call, dial (858) 384-5517, and enter conference ID number 13592848. A telephonic replay will be available from approximately 2:00 p.m. Eastern Time on the day of call through Wednesday, November 5, 2014. 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, the principal markets for Graham’s equipment are energy, including oil and gas refining and nuclear and other power generation, 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, shipbuilding, 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.

Forward-looking statements are subject to risks, uncertainties and assumptions and are identified by words such as “expects,” “estimates,” “confidence,” “projects,” “typically,” “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, the expected performance of Energy Steel & Supply Co, expected

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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 general economic conditions and customer behavior, forecasts regarding the timing and scope of the economic recovery in its markets, and its acquisition and growth strategy 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.

For more information contact:

FINANCIAL TABLES FOLLOW.

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Graham Corporation Second Quarter Fiscal 2015

Consolidated Statements of Operations—Unaudited

(Amounts in thousands, except per share data)

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Graham Corporation Second Quarter Fiscal 2015

Consolidated Balance Sheets—Unaudited

(Amounts in thousands, except per share data)

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Graham Corporation Second Quarter Fiscal 2015

Consolidated Statements of Cash Flows—Unaudited

(Amounts in thousands)

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Graham Corporation Second Quarter Fiscal 2015

EBITDA Reconciliation—Unaudited

(Amounts in thousands)

EBITDA is defined as consolidated net income before interest expense and income, income taxes, and depreciation and amortization. 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 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 EBITDA is a non-GAAP measure and is thus susceptible to varying calculations, EBITDA, as presented, may not be directly comparable to other similarly titled measures used by other companies.

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Graham Corporation Second Quarter Fiscal 2015

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 Second Quarter Fiscal 2015

Additional Information—Unaudited

(Continued)

SALES BY REGION FY 2015

($ in millions)

SALES BY REGION FY 2014

($ in millions)

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