Arthur attended Staunton Military Academy (class of 1922), Emory University in 1923-1924 and the University of Pennsylvania in 1925-1926. Arthur and Ruby Hazel Blair were married on 16 Oct 1937.
Arthur enlisted in L Company 116th Infantry of the Virginia National Guard in 1920 and rose to rank of SGT before being commissioned as a 2LT in 1928. He was promoted to 1LT in 1933 and to CPT in 1935. He was commanding L Company 116th Infantry when the unit was federalized/called to active duty on 3 Feb 1941. CPT Sheppe was promoted to MAJ in May 1941 commanding 3rd Battalion 116th Infantry and to LTC in November 1942 and was then made Executive Officer of the 175th Infantry Regiment with which unit LTC Sheppe went ashore at Omaha Beach on 7 Jun 1944. He replaced COL Warfield (who was killed) as commander of 2nd Battalion 115th Infantry on 12 Jun 1944 and commanded the battalion throughh to Saint-Lo. He was then reassigned to command 3rd Battalion 115th Infantry for a short time before again becoming Executive Officer of the 175th where he was serving at the time Brest was captured. Commissioned as a COL in the Regular Army in 1946 he commanded a regiment at Fort McClellan in Anniston, Alabama. He resigned after 3 months to return to civilian life. His awards during the war included the Silver Star and Bronze Star Medal with 3 oak leaf clusters. Virginia's Governor Battle asked him to return to service in 1947 to reorganize the 116th Infantry and he commanded the regiment until forced by a heart attack to retire in 1952. It was at that time that he was promoted to BG.
President of Gus Dull Transfer Company, ran for Staunton City Council in 1948, was manager of the Stillwater Worsted Mill near Craigsville, Virginia and participated in several community organizations. He was a member of Veterans of Foreign Wars, American Legion, Staunton Rotary Club, Circus Saints & Sinners and Country Club of Staunton.
After retirement, he worked as Veterans Claims Agent for the Veterans Administration. He was living at 1625 North Augusta Street in Staunton in 1974. BG Sheppe died at the Medical College of Virginia in Richmond, Virginia on 3 Jun 1974 and was interred at Thornrose Cemetery in Staunton, Virginia.