Exhibit 99.1

Graham Corporation 20 Florence Avenue Batavia, NY 14020

IMMEDIATE RELEASE

Graham Corporation Reports Strong Orders and Record

Backlog for Fiscal Year 2015 First Quarter

BATAVIA, NY, July 31, 2014 – Graham Corporation (NYSE: 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 first quarter ended June 30, 2014. Graham’s current fiscal year (“fiscal 2015”) ends March 31, 2015.

Mr. James R. Lines, Graham’s President and Chief Executive Officer, commented, “We had a solid start to fiscal 2015 and I believe we are on track to achieve our growth targets for the year. Margins during the quarter reflected both the project mix in backlog and the fact that we remain in the early stages of a recovery in our markets. We are encouraged that the recovery appears to be steadily advancing, which we believe is reflected in our strong and growing backlog. We continue to invest in our facilities, processes and people while at the same time reaching for opportunities to expand our growth potential.”

U.S. Chemical/Petrochemical Industry Drives Sales in Quarter

(refer to sales by industry and region in accompanying tables)

Net sales in the first quarter of fiscal 2015 were $28.5 million, up from net sales of $28.3 million in the first quarter of the fiscal year ended March 31, 2014 (“fiscal 2014”). Sales to the U.S. market were $22.2 million, or 78% of total sales, up $7.2 million, or 48%, from the prior year. This increase was driven by infrastructure investments in the North American chemical/petrochemical industry. International sales decreased to $6.3 million with lower sales compared with the prior year in nearly all international regions.

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 one to two year basis.

First Quarter Fiscal 2015 Operating Performance

Gross profit was $7.9 million, or 27.8% of sales, compared with $10.0 million, or 35.4% of sales, in the same period of the prior fiscal year and $7.4 million, or 28.4% of sales, in the trailing fourth quarter of fiscal 2014. Differences in product mix negatively impacted gross margin when compared with both the prior-year period and the trailing fourth quarter, and resulted in gross margins below what we anticipate for fiscal 2015.

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Selling, general and administrative (“SG&A”) expenses were $4.3 million, relatively consistent with the prior-year period. SG&A as a percent of sales decreased to 15.3% in the first quarter of fiscal 2015 compared with 15.6% in the prior-year period.

Operating profit in the first quarter was $3.6 million, or 12.6% of sales, compared with $5.6 million, or 19.9% of sales, in the first quarter of fiscal 2014. When compared with the trailing fourth quarter of fiscal 2014, operating profit was up from $3.2 million, reflecting a 40 basis point improvement in operating margin.

Earnings before interest, taxes, depreciation, and amortization (“EBITDA”) was $4.2 million, or 14.6% of sales, compared with $6.2 million, or 21.8% of sales, in the same period of the prior fiscal year and $3.7 million, or 14.3% of sales, in the trailing fourth quarter. 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 important disclosures regarding Graham’s use of EBITDA as well as a reconciliation of net income to EBITDA.

Net income was $2.4 million, or $0.24 per diluted share, compared with $3.8 million, or $0.38 per diluted share, in the prior year’s first quarter.

Strong, Flexible Balance Sheet to Support Growth

Cash, cash equivalents and investments at June 30, 2014 were $61.4 million compared with $61.1 million at March 31, 2014.

Cash provided by operations in the first quarter of fiscal 2015 was $3.2 million, up from $2.0 million of cash provided by operations during the first quarter of fiscal 2014. The increase was driven primarily by a reduction in working capital usage during the fiscal 2015 quarter.

Capital expenditures were $2.6 million in the first quarter of fiscal 2015 compared with $0.3 million in first quarter of fiscal 2014. The majority of the increase was related to the ongoing capacity expansion at the Company’s Batavia, New York facility, which is on track for completion in the second quarter of fiscal 2015. Capital expenditures in fiscal 2015 are expected to be in the range of $5.5 million to $6.0 million, of which approximately 60% is expected to be utilized for the Batavia expansion.

Graham had no borrowings outstanding under its credit facility or any long-term debt outstanding at June 30, 2014.

Strong Pipeline of Opportunities and Increasing Bid Activity

Orders during the first quarter of fiscal 2015 were $31.1 million, compared with $32.8 million during the prior-year first quarter and $23.5 million in the trailing fiscal 2014 fourth quarter. Compared with the trailing quarterly period, the Company’s refining and chemical/petrochemical industry markets each had higher order levels, while orders for the power industry and its other commercial and industrial markets were down. During the first quarter of fiscal 2015, orders of $16.4 million, or 53%, were from U.S. customers, while orders from international markets accounted for $14.7 million of total orders, driven by sales to Canada, Asia and South America.

Graham expects that order levels will be variable between quarters, but that in the long-run orders will be relatively balanced between domestic and international markets.

The Company’s backlog was $114.8 million at June 30, 2014 compared with $112.1 million at March 31, 2014 and $90.4 million at June 30, 2013. Approximately 32% of projects in backlog at the end of the fiscal 2015 first quarter were for refinery projects, 27% were related to chemical and petrochemical projects, 13% were for power projects, including nuclear energy, 23% were for the defense industry and the remaining 5% were related to other industrial or commercial applications.

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Approximately 70% to 75% of orders currently in backlog are expected to be converted to sales within the next 12 months. Graham had no projects on hold in backlog as of June 30, 2014.

Fiscal 2015 Outlook Remains Unchanged

Graham continues to expect fiscal 2015 sales will be in a range of $120 to $130 million, representing anticipated growth of approximately 17% to 27% compared with fiscal 2014. Gross margin for fiscal 2015 is expected to be between 30% and 32%, as pricing power is still consistent with historic early-cycle margins. SG&A expense is expected to be between 15% and 16% of sales for fiscal 2015. Graham expects its fiscal 2015 full year tax rate to be between 33% and 34%.

Mr. Lines concluded, “The strong bidding activity we experienced during fiscal 2014 has continued into fiscal 2015 and we expect that order levels will remain strong. We believe that our key end markets of oil refining, petrochemical and other related energy markets are improving. We further believe that the current activity level within our pipeline continues to be more robust than in past expansion cycles, providing us opportunities to reach our goals for fiscal 2015 and beyond.”

Webcast and Conference Call

Graham will host a conference call and live webcast today at 2:00 p.m. Eastern Time to review its financial condition and operating results for its first quarter 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 1-201-689-8560. Alternatively, the webcast can be monitored on Graham’s website at www.graham-mfg.com.

To listen to the archived call, dial 1-858-384-5517, and enter replay pin number 13585606. A telephonic replay will be available from approximately 5:00 p.m. Eastern Time on the day of call through Thursday, August 7, 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,” “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 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

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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 First Quarter Fiscal 2015

Consolidated Statements of Operations—Unaudited

(Amounts in thousands, except per share data)

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Graham Corporation First Quarter Fiscal 2015

Consolidated Balance Sheets—Unaudited

(Amounts in thousands, except per share data)

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Graham Corporation First Quarter Fiscal 2015

Consolidated Statements of Cash Flows—Unaudited

(Amounts in thousands)

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Graham Corporation First 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 First 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 First 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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