Bernard J. Vierling, 68, a retired research and development official of the Federal Aviation Administration and the Urban Mass Transit Administration, died of cancer Dec. 27 at Sibley Memorial Hospital.

Mr. Vierling was born in Bakersfield, Calif., and earned a bachelor's degree in mechanical engineering at Stanford University. In 1941, he moved to Washington as chief engineer for Penn Central Airlines. He later was president of Aircraft Advisers and from 1948 to 1962 he was a partner in the Aircraft Supply Corp.

In 1962, he joined the FAA as director of systems maintenance service. In 1965, he was named deputy director of the agency's supersonic transportation development program. In 1971, he transferred to the Urban Mass Transit Administration, where he directed a pilot project in Morgantown, W. Va. He later was director of bus and rail research and development. In 1979, when he retired, he was director of research and development for buses and paratransit, which provides transportation for the handicapped.

In 1964, Mr. Vierling received an award from President Johnson for effecting economies. In 1973, he received the secretary of Transportation's award.

Mr. Vierling was a founder and former president of the National Aviation Club and a member of the National Aeronautics Association, the Aero Club, the Air Force Association and the Belle Haven Country Club. He lived in Alexandria until moving to his farm in Flint Hill, Va., in 1979.

Survivors include his wife, the former Martha Jane Peairs, of Flint Hill; three children, Lawrence B. of Fairburn, Ga., Bruce W. of Flint Hill, and Karen J. Allen of Oak Park, Ill.; a sister, Helen Wilt of Rancho Cordova, Calif., and five grandchildren.