Mary Elizabeth Metcalf, 57, who operated a tutoring service in Fairfax County for nearly 20 years, died of cancer yesterday at the Fairfax Nursing Center.

Miss Metcalf taught high school in St. Marys County and Annapolis before moving to Fairfax County in 1950. She then worked with retarded children in the county school system and directed a Girl Scout troop for the retarded.

In the late 1950s, before Fairfax County initiated a kindergarten program, she held classes there for pre-school children.

During the late 1960s, Miss Metcalf was active with the Visiting Nurse Service of Fairfax and served as its treasurer for many years. She also had been a member of its board of directors.

She was born in Galion, Ohio, and grew up in St. Marys County. In 1941, she graduated from the old Normal State College in Towson.

Miss Metcalf was a member of the board of Church Women United (formerly the Council of United Church Women). She had been a member of Good Shepherd Episcopal Church for about seven years and previously had attended Truro Episcopal Church in Fairfax.

Survivors include a brother, Francis O. H. Metcalf, of the home in Fairfax.

It is suggested that expressions of sympathy be in the form of contributions to Good Shepherd Episcopal Church in Fairfax.