Exhibit 99.1

Graham Corporation    20 Florence Avenue    Batavia, NY 14020

IMMEDIATE RELEASE

Graham Corporation Reports

Record Revenue for Fiscal 2013

BATAVIA, NY, May 31, 2013 – 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 fourth quarter and fiscal year ended March 31, 2013 (“fiscal 2013”).

Net sales in the fourth quarter of fiscal 2013 were $30.9 million, up from net sales of $20.3 million in the fourth quarter of the fiscal year ended March 31, 2012 (“fiscal 2012”), with the increase driven primarily by international sales. Higher volume and improved margins drove net income to $4.1 million, or $0.41 per diluted share, compared with $0.4 million, or $0.04 per diluted share, in the prior-year’s fourth quarter.

Fiscal 2013 net sales of $105.0 million increased by $1.8 million, or 1.7%, over net sales of $103.2 million in fiscal 2012. Net income in fiscal 2013 was $11.1 million compared with net income of $10.6 million in fiscal 2012, an increase of $0.6 million, or 5.6%. Per diluted share, fiscal 2013 earnings were $1.11 compared with $1.06 in the prior year. Fiscal 2013 included a $975 thousand, or $0.10 per diluted share, benefit from the reversal of the earn-out reserve related to Graham’s wholly-owned subsidiary Energy Steel & Supply Co. Excluding this benefit, fiscal 2013 adjusted net income was $10.2 million, or $1.01 per diluted share.

Mr. James R. Lines, Graham’s President and Chief Executive Officer, commented, “We executed well in 2013 and delivered solid results while operating in what to date has been a modest market recovery. During a rather moderate market, our team effectively influenced what was within their control to drive top line growth and earnings.”

- MORE -

Graham Corporation Reports Record Revenue for Fiscal 2013

May 31, 2013

Page 2 of 11

Increased Refining Shipments Drove Improved Revenue in Fourth Quarter

International sales increased by 87%, or $6.7 million, to $14.5 million in the fiscal 2013 fourth quarter compared with the same prior-year period. Sales improved across all regions, particularly in Asia and the Middle East. Fourth quarter sales to the U.S. market were $16.4 million, or 53% of total sales, up $3.9 million, or 31.6%, compared with $12.5 million in the same prior-year period.

Fourth Quarter Fiscal 2013 Sales by Industry

($ in millions)

Refining industry sales more than tripled in the fourth quarter of fiscal 2013 compared with the prior-year period on higher demand for Graham’s engineered-to-order products, primarily in China. Higher sales to the power market reflect advancing projects in backlog for new build nuclear facilities. Increased sales to other commercial and industrial markets were primarily related to the progress made on the Naval Nuclear Propulsion Program (“NNPP”) orders in backlog. Lower sales to the chemical/petrochemical market were mostly associated with project timing.

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.

Fourth Quarter Operating Performance

Gross profit was $10.5 million, or 34.1% of sales, in the fourth quarter of fiscal 2013 compared with $5.2 million, or 25.6% of sales, in the same period of the prior fiscal year and compared with $7.1 million, or 27.8% of sales, in the trailing third quarter of fiscal 2013. The improvements in gross profit and margin compared with the same prior-year quarter and the trailing third quarter were the result of both higher volume and sales of aftermarket products.

Selling, general and administrative (“SG&A”) expenses in the fourth quarter of fiscal 2013 were $4.9 million, up from $3.6 million in the prior-year period. SG&A as a percent of sales improved to 15.7% in the fourth quarter of fiscal 2013 compared with 17.9% in the prior-year period.

Operating profit in the fourth quarter of fiscal 2013 was $5.7 million, or 18.4% of sales, compared with $1.6 million, or 7.7% of sales, in the fourth quarter of fiscal 2012.

Earnings before interest, taxes, depreciation, and amortization (“EBITDA”) was $6.2 million, or 20.1% of sales, in the fourth quarter of fiscal 2013 compared with $2.1 million, or 10.5% of sales, in the same period of the prior fiscal year. 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.

- MORE -

Graham Corporation Reports Record Revenue for Fiscal 2013

May 31, 2013

Page 3 of 11

Graham’s effective tax rate for the fourth quarter of fiscal 2013 was 28.1% compared with 68.2% in the same prior-year period. The lower tax rate in fiscal 2013 includes research and development (“R&D”) related tax credits retroactive to the start of the fiscal year, due to the extension of the credit in January 2013. The prior-year’s effective tax rate was impacted by adjustments related to a settlement with the IRS.

Fiscal 2013 Full Year Review

Net sales for fiscal 2013 were $105.0 million, up from $103.2 million in fiscal 2012. International sales were $49.3 million and represented 47% of total sales in fiscal 2013 compared with $47.8 million, or 46% of total sales, in fiscal 2012. Compared with fiscal 2012, U.S. sales increased by $0.3 million, or 0.5%, to $55.7 million for fiscal 2013.

Gross profit for fiscal 2013 declined to $31.8 million, or 30.3% of total sales, compared with $32.6 million, or 31.6% of sales, in the same prior-year period. Lower gross profit in fiscal 2013 reflected lower relative margins in the first half of fiscal 2013, a trend that reversed during the second half of the fiscal year. On a comparative basis, the first half of fiscal 2012 benefitted from higher margin projects which were won during the last up cycle.

SG&A expenses of $16.6 million in fiscal 2013 were up from $15.5 million in fiscal 2012. As a percentage of sales, SG&A was 15.8% in fiscal 2013 compared with 15.1% in the prior fiscal year. Excluding the impact of the $975 thousand earn-out reserve reversal related to Energy Steel in the third quarter of fiscal 2013, adjusted SG&A for fiscal 2013 was $17.5 million. Adjusted SG&A as a percent of fiscal 2013 sales was 16.7%.

EBITDA for fiscal 2013 was $17.3 million, or 16.5% of sales, compared with $19.1 million, or 18.5% of sales, in fiscal 2012. See the attached tables for important disclosures regarding Graham’s use of EBITDA as well as a reconciliation of net income to EBITDA.

Strengthened Balance Sheet with No Debt

Cash flow used in operations in the fourth quarter of fiscal 2013 was $2.5 million compared with $1.3 million in the fourth quarter of fiscal 2012. Cash provided by operations in fiscal 2013 was $12.4 million, up from $2.6 million of cash provided by operations during fiscal 2012. The increase in cash provided by operations in fiscal 2013 was primarily related to improvements in working capital requirements.

Cash, cash equivalents and investments at March 31, 2013 increased to $51.7 million compared with $41.7 million at March 31, 2012. When compared with December 31, 2012, cash, cash equivalents and investments were down by $3.4 million from $55.1 million.

Capital expenditures were $0.7 million in the fourth quarter of fiscal 2013 compared with $0.6 million in the fourth quarter of fiscal 2012. For fiscal 2013, capital expenditures were $1.7 million compared with $3.2 million in fiscal 2012. Capital expenditures in fiscal 2014 are expected to be in the range of $3.5 million to $4.5 million, with the upper end of the range likely to be spent only upon successfully securing orders for the U.S. Navy submarine program.

Graham had neither borrowings outstanding under its credit facility nor any long-term debt at March 31, 2013.

Strong Pipeline of Opportunities and Increasing Bid Activity

Mr. Lines concluded, “We remain encouraged by the quality and quantity of bidding activity for the significant number of what appear to be funded and viable energy industry projects. These expected projects include new petrochemical and fertilizer capacity, new coal to liquids and gas to liquids facilities, refining investments and investments in power generation markets. Our commitment to realizing our near-term strategy to double Graham across this expansion cycle is unchanged. While in the midst of the present modest recovery phase in our markets, it remains difficult to predict order timing. The recent subdued nature of our markets, in my view, is solely a timing issue and not related to fundamentals.”

- MORE -

Graham Corporation Reports Record Revenue for Fiscal 2013

May 31, 2013

Page 4 of 11

Orders during the fourth quarter of fiscal 2013 were $25.9 million, down 39% from $42.3 million in the fourth quarter of fiscal 2012 which had a surge of orders from the nuclear power and refining markets. When compared with the trailing third quarter of 2013, orders were up 5% from $24.6 million. Compared with the same prior-year period, orders in the fourth quarter from the power market were down by $9.2 million to $4.2 million, orders from the chemical/petrochemical market decreased by 4.5 million to $3.1 million and refining market orders decreased by $4.1 million to $14.8 million. Orders from other industrial and commercial markets during the fourth quarter of fiscal 2013 were up by $1.5 million to $3.8 million when compared with the same prior-year period.

Orders from U.S. customers represented 58%, or $15.0 million, of total orders during the fourth quarter of fiscal 2013, while orders from international markets accounted for $10.9 million of total orders. Graham expects that orders will continue to be variable between quarters, but that in the long-run orders will be relatively balanced between domestic and international markets.

Graham’s backlog was $85.8 million at March 31, 2013 compared with $90.7 million at December 31, 2012 and $94.9 million at March 31, 2012. Approximately 40% of projects in backlog as of the end of the fourth quarter were for refinery projects, 25% were for power projects, including nuclear, and 8% were for chemical and petrochemical projects. All other industries served by Graham accounted for 27% of backlog.

Approximately 75% to 80% 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 March 31, 2013.

Graham expects sales will be in a range of $100 million to $115 million in fiscal 2014. Gross margin for fiscal 2014 is expected to be between 29% and 31% as backlog is expected to continue to reflect moderate recovery levels of its end markets. SG&A expense is expected to be between 15% and 16% of sales for fiscal 2014. Graham expects its fiscal 2014 full year tax rate to be within a range of 33% to 34%.

Webcast and Conference Call

Graham 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 fiscal 2013, 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 412392. A telephonic replay will be available from approximately 2:00 p.m. Eastern Time on the day of call through Friday, June 7, 2013. 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 more than 77 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.

- MORE -

Graham Corporation Reports Record Revenue for Fiscal 2013

May 31, 2013

Page 5 of 11

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,” “plan,” 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 nuclear power generation 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 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 and Quarterly Reports 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.

- MORE -

Graham Corporation Reports Record Revenue for Fiscal 2013

May 31, 2013

Page 6 of 11

Graham Corporation Fourth Quarter and Fiscal 2013

Consolidated Statements of Operations

(Amounts in thousands, except per share data)

- MORE -

Graham Corporation Reports Record Revenue for Fiscal 2013

May 31, 2013

Page 7 of 11

Graham Corporation Fourth Quarter and Fiscal 2013

Consolidated Balance Sheets

(Amounts in thousands, except per share data)

- MORE -

Graham Corporation Reports Record Revenue for Fiscal 2013

May 31, 2013

Page 8 of 11

Graham Corporation Fourth Quarter 2013

Consolidated Statements of Cash Flows

(Amounts in thousands)

- MORE -

Graham Corporation Reports Record Revenue for Fiscal 2013

May 31, 2013

Page 9 of 11

Graham Corporation Fourth Quarter and Fiscal 2013

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 of 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.

- MORE -

Graham Corporation Reports Record Revenue for Fiscal 2013

May 31, 2013

Page 10 of 12

Graham Corporation Fourth Quarter Fiscal 2013

Additional Information

ORDER & BACKLOG TREND

($ in millions)

SALES BY INDUSTRY FY 2013

($ in millions)

SALES BY INDUSTRY FY 2012

($ in millions)

- MORE -

Graham Corporation Reports Record Revenue for Fiscal 2013

May 31, 2013

Page 11 of 11

Graham Corporation Third Quarter Fiscal 2013

Additional Information

(Continued)

SALES BY REGION FY 2013

($ in millions)

SALES BY REGION FY 2012

($ in millions)

- END -