Exhibit 99.1

STONE ENERGY CORPORATION
Announces 10% Increase in Capital Spending; To Present at Lehman Brothers Energy Conference 

NYSE — SGY
LAFAYETTE, LA. September 3, 2004

        Stone Energy today announced that its board of directors recently authorized a 10% increase in capital spending for 2004. With the increase, the current 2004 capital expenditures budget is now $310 million, which excludes acquisitions and capitalized interest and overhead expenses.

        Stone also announced that its President and Chief Executive Officer, David H. Welch, will present at the Lehman Brothers 2004 CEO Energy/Power Conference at the Waldorf Astoria Hotel in New York on Tuesday, September 7^th at approximately 2:25 p.m. eastern time. The presentation materials will be available in the “Event” section of the Company’s Web site, www.stoneenergy.com, within 24 hours of the presentation.

        Stone Energy is an independent oil and gas company headquartered in Lafayette, Louisiana, and is engaged in the acquisition and subsequent exploration, development and operation of oil and gas properties located in the Gulf Coast Basin and Rocky Mountains. For additional information, contact James H. Prince, Chief Financial Officer, at 337-237-0410-phone, 337-237-0426-fax or via e-mail at princejh@StoneEnergy.com.

        Certain statements in this press release are forward-looking and are based upon Stone Energy’s current belief as to the outcome and timing of future events. All statements, other than statements of historical facts, that address activities that Stone Energy plans, expects, believes, projects, estimates or anticipates will, should or may occur in the future, including future production of oil and gas, future capital expenditures and drilling of wells and future financial or operating results, are forward-looking statements. Important factors that could cause actual results to differ materially from those in the forward-looking statements herein include the timing and extent of changes in commodity prices for oil and gas, operating risks and other risk factors as described in Stone Energy’s Annual Report on Form 10-K as filed with the Securities and Exchange Commission. Should one or more of these risks or uncertainties occur, or should underlying assumptions prove incorrect, Stone Energy’s actual results and plans could differ materially from those expressed in the forward-looking statements.