Following his graduation from law school, Matheson practiced law for several years in Cedar City, Utah. In the mid-1950s he moved to Salt Lake City and became Deputy Salt Lake County Attorney. He joined the legal department of the Union Pacific Railroad Company in 1958 and, except for a three-year period from 1969 to 1971 when he was assistant general counsel for the Anaconda Copper Company, remained there until 1976, when he was elected Governor of Utah on the Democratic ticket, defeating Utah Attorney General Vernon B. Romney.