Ralph A.Beeton, 51, a Northern Virginia banker who was active in civic and professional organizations, died of cancer Sunday in his Arlington home.

He had retired as chairman and chief executive of First Virginia Banks Inc; a bank holding company based in Falls Church, in December 1978, for reasons of heaith.

Mr. Beeton joined the bank in 1957 and was elected president of First Virginia in 1962. He became chief executive five years later. 'e served on the board of directors until his death.

In 1974, Gov. Mills E. Godwin appointed him the Northern Virginia representative on the State Highway and Transportation Commission. He retired earlier this year for reasons of health.

He also had been a menber of the Governor's Advisory Board on Reveune Estimates and on the Virginia Housing Development Authority during the 1970s.

He was elected as the first president of the Virginia Mental Health Foundation, which was incorporated in 1971 as a joint project of the Virginia Federation of Women's Clubs and the State Department of Hygiene and Hospitals.

Mr. Beeton was president of the Virginia Bankers Association from 1975 to 1976, then served a year as chairman of the Association of Bank Holding Companies. He was the Virginia vice president of the American Bankers Association and a member of the ABA's governing Council.

He was a trustee of the Virginia foundation of Independent Colleges and Randolph-Macon College from 1972 to 1974.

For several years, he had been treasurer and a member of the board of Wolf Trap Associates.

Mr. Beeton was born in Alexandria. He was a 1945 graduate of Roosevelt High School in Washington. He earned a bachelor's degree in economics and a law degree at the University of Virginia.

Prior to joining First Virginia, Mr. Beeton served in the Navy and worked for a time for International Harvester in Richmond.

He was a member of American, Virginia, and Arlington county bar associations. He belonged to the Cosmos Club and held memberships in the Washington Golf and Country Club and the Farmington Country Club.

Mr. Beeton was a member of Mount Loivet United Methodist Church in Arlington.

Survivors include his wife, the former Virginia Holland, two sons, Thomas and William, and two daughters, Sarah and Charlotte, all of the home; his parents, Mr. and Mrs. Frank E. Beeton Sr., of Falls Church; a brother, Frank E. Jr., of Fairfax, and seven sisters, Kathleen B. Butler, of Charlotte, N.C., Helen B. Fines, of Manassas, Jane B. Bouteliier, of McLean, Frances B. Kane, of Luray, Paruline B. Ambrogi, of Vienna, Nancy B. Fritz, of Clearwater, Fla., and Beth B. Vice, of Collinsville, Okla.