Elliott Mitchell earned a B.S. in chemistry from William and Mary in 1941 and served from 1942 to 1950 as a physical chemist and chemical engineer in the Department of the Navy. From then until 1958 he was physical sciences administrator and then chief of propulsion research and development in the Navy's Bureau of Ordnance. In 1958 he joined NASA as chief of the solid rocket development program. When he left NASA in 1961, he was assistant director of manned space flight programs for propulsion. Thereafter, he became a consultant.