Ph.D. University of Chicago, Illinois, 1930
McShane spent most of his academic career at the University of Virginia, from 1935 to 1974. McShane is famous for his work in the calculus of variations, integration theory, stochastic calculus, and exterior ballistics. During World War II, from 1942-45, he was head of the Ballistics Research Laboratory at the Aberdeen Proving Ground, Maryland, and his joint treatise, Exterior Ballistics, written during this period and published in 1953, was considered the leading work on ballistics at the time. He also served as president of the Mathematical Association of America from 1953-54, and took an active interest in undergraduate mathematics. McShane was a member of the U.S. National Academy of Sciences.