Mr. and Mrs. Walter Booth Brooks III, and Mr. Edmund Sheedy, all of Palm Beach, Fla., announce the engagement of their daughter, Laurelle Foote Sheedy to Robert Trimble Mathis, son of Mr. and Mrs. John Harris Mathis of Port Haywood, Va.

Miss Sheedy is a graduate of Stephens College (Mo.) was presented by the Junior Assembly at the Everglades Club in Palm Beach and has also served as staff assistant to Presidents Nixon and Ford. Her grandparents are the late Dr. and Mrs. Bryan de Forest Sheedy of New York City and her stepfather is the son of the late Mrs. Louise Cromwell Heiberg of Washington, D.C. and the late Walter B. Brooks Jr. of Baltimore.Mr. Mathis is a graduate of Columbia University and was a first lieutenant in the U.S. Army. His father, now retired, was the chairman and chief executive officer of Lone Star Industries and his grandparents are the late Mr. and Mrs. Monro Cadmus Mathis of McAlester, Okla.

Mr. Mathis is first vice-president of the investment banking firm of Blyth Eastmand Dillon & Co., where Miss Sheedy is an associate in the corporate finance department. Both have master's in business administration from Harvard University. They plan to be married in New York City on October 20.