Paul J. May Jr., 55, a former building engineer for the Aldon Management Corp., died of cancer Monday at the Veterans Administration Hospital in Washington.

He had worked for the firm, which builds, owns and manages apartment and office buildings in the Washington area, from 1971 to 1978. He handled engineering problems in a number of Aldon buildings.

Mr. May was a fifth-generation Washingtonian. He graduated from Mount Saint Joseph College High School in Baltimore and entered Mount Saint Mary's College in Emmitsburg, Md., before World War II.

During the war, he served as a cyptographic technician with the Army and participated in a number of major European battles. He returned to Mount Saint Mary's after the war, graduating in about 1946.

Before joining Aldon's, Mr. May had worked for the Investment Building and Ruppert Real Estate.

He belonged to the American Legion and Knights of Columbus. He was a member of the Potomac River Power Squadron, secretary of District Five of the U.S. Power Squadron and a former commodore of the Chesapeake Cruiser Association.

A former resident of Washington, where he had been active in the Catholic Shrine of the Most Blessed Sacrament, Mr. May moved to Edgewater, Md., about four years ago. He belonged to Our Lady of Perpetual Help parish there.

He is survived by his wife, Carol, of the home; 13 children, Paul Edward, Raymond, Bunny, Michael, Andrew, Candy Finch, and Shirley Goodson, all of Gaithersburg, Patrick, of Wichita, Kan., Kathleen Foster, of Seabrook, Md., Susan Wofford, of Gold Beach, Ore., Karen Boyd, of Columbia, S.C., and Jaetn and Jill both of Arkansas; his parents, Mr. and Mrs. Paul May Sr., of Washington; a sister, Rose Mary Splain, of Washington, and eight grandchildren.