Exhibit 99.1

STONE ENERGY CORPORATION
Announces Retirement of Joe R. Klutts from Board of Directors 

NYSE — SGY
LAFAYETTE, LA. May 24, 2004

        Stone Energy Corporation today announced that Joe R. Klutts has elected to retire from the Company’s Board of Directors effective May 20, 2004. Mr. Klutts has been associated with Stone and its predecessors for over 30 years. His leadership was an important part of Stone Energy’s transformation from a small private oil and gas venture into a public company. Mr. Klutts served the Company as its first President until February 1994 when he was named vice chairman of the Board. Also, he has served on the Company’s Board of Directors since its inception in 1993.

        “It has been a pleasure working with Joe during his long association with our company and its predecessors,” said James H. Stone, chairman of the board. “We thank him for all of his contributions and wish him well in his future endeavors.”

        Stone Energy is an independent oil and gas company headquartered in Lafayette, Louisiana, and is engaged in the acquisition and subsequent exploitation, 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.