Theodore Roosevelt Farrington, 56, an engineer and elvillian official of the Air Force Department, died of lymphomas Monday at Arlington Hospital.

He was A-7D program manger of the Air Force Systems Command at the time of his death. He had joined the Air Force A-7 project office here in 1968.

Bron in Watertown, N.Y., Mr. Farrington attended Clarkson Technical College in Potsdam, N.Y., and graduated from Rensselaer Polytechnic Institute as an aeronautical engineer in 1943.

During World War II, he served as an aircraft technical sergeant with the U.S. Army Air Forces.

After the war, Mr. Farrington held various civilian engineering positions with the Air Force Material Command at Wright-Patterson Air Force Base in Ohio. He received a Meritorious Civilian Service Award for his work in hydraulic controls and in-flight refueling.

He was a member of the Society of Aeronautical Engineers.

He is survived by his wife, Emily Willis Farrington, of the home in Alexandria; five sons, Jon, of the Home, Craig and Kirk, both students at the University of Washington, Gary, of Blaine, Wash., and Keith, a student at Pratt Institute of Art in New York, and two brothers, Navy Capt. Robert F., of Fort Washington, Md., and David P., of Haworth, N.J.

The family suggests that expressions of sympathy may be in the form of contributions to the Mount Vernon, Presbyterian Church in Alexandria or the Campership Fund of North Country Campus in New York City.