He received his bachelor of engineering and bachelor of science degrees from Tulane University in 1925, following with a M.S. degree from Tulane in 1927. McShane received his Ph.D. in mathematics from the University of Chicago.[2][3] He taught at the University of Virginia for 39 years until he retired in 1974. His doctoral students include Victor Klee, Billy James Pettis, and David Lowdenslager, who collaborated with Henry Helson.