Hugh Cragg Farthing (July 17, 1892 – June 8, 1968) was a provincial level politician from Alberta, Canada. He served as a member of the Legislative Assembly of Alberta from 1930 until 1935 representing the electoral district of Calgary.He was educated at Kingston Collegiate Institute and McGill University, where he was a member of The Kappa Alpha Society. His education at McGill was interrupted by service in World War I.