Muriel R. Harris, 85, the chairman of the board of L. E. Harris Agency, Inc., a Washington insurance brokerage, died of cardiac arrest Monday at her home in Washington.

The firm was founded by Mrs. Harris's husband, Lt. Col. Louis E. Harris, in 1922. When Col. Harris went on active military duty in World War II, Mrs. Harris became president of the company. She held that position until 1978, when Col. Harris died. She then was named chairman of the board. Despite failing sight, she remained active in the business until her death.

Mrs. Harris was born in Indianapolis and moved to Washington as a girl. She was a graduate of Central High School. Following her marriage, she was active in church and community affairs here and from 1938 to 1942, when she became head of the family business, she was chairman of the American Red Cross D.C. Motor Corps.

Survivors include a son, Jerome J. Harris of Burtonsville, now the president of the company; a daughter, Ruth Ann Allen of Washington, four grandchildren, and two great-grandchildren.

The family suggests that expressions of sympathy be in the form of contributions to The First Church of Christ, Scientist, Boston, or to The Washington Star, Silver Spring, a closed-circuit radio broadcast for the blind.