Leroy S. Bendheim, 81, a two-term mayor of Alexandria and three-term Virginia state senator whose political career spanned more than 40 years, died of cancer June 18 at Alexandria Hospital.

Mr. Bendheim, a Democrat, also served on the Alexandria School Board from 1934 to 1943, and was chairman for five of those years. He was on the City Council from 1948 to 1952. He was vice mayor from 1952 to 1955, then served two three-year terms as mayor before his defeat in 1961 by Frank E. Mann.

Mr. Bendheim was elected to the Virginia Senate in 1963, and served there 12 years before losing in a bid for a fourth term to Republican Wiley F. Mitchell Jr., then the vice mayor of Alexandria.

As a state senator, Mr. Bendheim tended to concentrate on finances and such bread-and-butter issues as taxes; as Alexandria's mayor, he worked on development, urban renewal and holding down utility rates; and as a City Council member, he worked on such matters as off-street parking in the Old Town area.

In 1968 he was named chairman of a prestigious 15-member state committee that spent two years studying Virginia's tax structure and looking for ways to finance the growing demands on the state government. The panel eventually reported that Virginia could finance a 25 percent budget increase through routine expansion of existing revenue sources, budgetary surpluses and unexpended appropriations, and that no tax increase was necessary.

Mr. Bendheim's years as mayor coincided with the turbulence of the early civil rights movement and Virginia's massive resistance to school desegregation, but he generally kept a low profile on those issues. He appointed a biracial commission that helped bring about an orderly desegregation of department store lunch counters in Alexandria in 1960, and he urged passage of a local compulsory school attendance law after the Virginia General Assembly enacted legislation permitting localities to close public schools rather than desegregate.

When the rabbi of Alexandria's Temple Beth El, of whose board of trustees Mr. Bendheim was president, was criticized for denouncing massive resistance in a Yom Kippur homily, Mr. Bendheim declined to discuss his views of the rabbi's remarks.

A native and lifelong resident of Alexandria, Mr. Bendheim was a graduate of Central High School in Washington. He graduated from George Washington University where he also earned a law degree. He opened a private law practice in Alexandria in 1929 and taught at GWU law school. During World War II he served in the Army in Europe.

He was senior partner of the law firm of Bendheim, Fagelson, Bragg and Giammittorio.

Mr. Bendheim was a past commander of the Virginia Veterans of Foreign Wars and a former president of the Alexandria Bar Association.

Survivors include his wife of 53 years, Ethel Coleman Bendheim of Alexandria.