Joseph Wesp was enlisted in the Reserve Corps in March 1942, while an advanced Reserve Officer Training Corps student at Texas A & M College, and was called to active duty prior to graduation. After the war he entered Baylor University School of Medicine in Houston, Texas, and graduated with a medical degree in May 1947. Following his postgraduate specialty training, General Wesp was commissioned a first lieutenant in the U.S. Air Force Medical Service in October 1950. He retired in 1980 as a U.S. Air Force Brigadier General.