His father, Patrick F. Kavanagh, was an Irish immigrant and laborer and electrical worker for a New York city streetcar company; his mother, Anna C. Unger, came from Germany.
He then started work as a structural designer for engineering firms in New York and Pennsylvania on railway and highway bridges, sanitary plants, power plants, electrical transmission towers, waterfront structures, floating docks, and refineries, and during World War II was an aircraft engineer.
In 1953 he began consulting for Praeger & Maguire, which was renamed Praeger-Kavanagh when he became partner, and later Praeger-Kavanagh-Waterbury.
Kavanagh was responsible for several major engineering projects, including the Arecibo radio telescope in Puerto Rico, the Hawkins Point Floating Bridge on the St. Lawrence River, plans for the subway system of Caracas, and the Long Island Sound bridge crossing.
Among his many honors he received the Ernest E. Howard Award from the American Society of Civil Engineers; the David Steinman Medal for Structural Engineering from the City College of New York; the Gold Medal of the Architectural League of New York; and an Honorary Life Membership in the New York Academy of Sciences.