Robert E. Sher, 77, a Washington lawyer for 45 years who specialized in antitrust law, died Tuesday at Georgetown University Hospital. He had a heart ailment.

A graduate of the University of Wisconsin's law school, Mr. Sher had a private law practice in his native Superior, Wis., for seven years before moving to Washington in 1933.

He was a lawyer for the Agriculture Department and a special assistant to the attorney general in the Justice Department's antitrust division before beginning his private law practice here in 1941. He retired two years ago.

Mr. Sher, who lived in Washington, was a past president of the Jewish Social Service Agency and Jewish Foster Home and a past president of the Washington chapter of the American Jewish Committee. He was a member of the Washington Hebrew Congregation and Woodmont Country Club in Rockville.

A student of history and political affairs, he was an authority on the Civil War. He also had been active in Democratic Party politics.

Survivors include his wife of 51 years, the former Pearl Wolpert, of Washington; a son, Allan L., of Scardale, N.Y.; a daughter, Elizabeth Schnayerson of Berkeley, Calif.; two sisters, Ruth Sher of Superior, and Carol Sher of Los Angeles, and five grandchildren.