Henry Goodrich earned the BS in civil engineering from UT in 1943. Upon discharge from the Navy Engineer Corps, he accepted a position with Rust Engineering Company in Birmingham. In 1968 he joined Inland Container Corporation as executive vice president and director and became president and CEO in 1970, a position he held until 1979. In 1980 he returned to Birmingham to become president and CEO of Southern National Resources, which he renamed SONAT. He stepped down as chief executive officer in 1984 but remained as chairman of the board through 1985. Goodrich was a director of 35 companies, 9 of which were listed on the New York Stock Exchange.
In 1975 Pulp and Paper named him Papermaker of the Year. In 1981 he was named Best Chief Executive in the Gas Pipeline Industry. He was a key member of the UT Development Council, and in 1973 he received the Nathan W. Dougherty Award from the College of Engineering. He was a member of the American Society of Civil Engineers and held honorary doctorate degrees from Butler University, 1976; Birmingham Southern College, 1985; University of Alabama at Birmingham, 1986; and Marion College, 1978. In 1984 he was inducted into the Alabama Academy of Honor. In 1985 the Sonat/Mizui semisubmersible oil-drilling unit was named for him.