Edward James McShane (May 10, 1904 – June 1, 1989) was an American mathematician noted for his advancements of the calculus of variations, integration theory, stochastic calculus, and exterior ballistics.

[2][3][4][5] His name is associated with the McShane–Whitney extension theorem[6] and McShane integral.

McShane was professor of mathematics at the University of Virginia,[2][4] president of the American Mathematical Society,[2][3][5] president of the Mathematical Association of America,[5] a member of the National Science Board[5] and a member of both the National Academy of Sciences and the American Philosophical Society.

His doctoral students include Victor Klee, Billy James Pettis, and David Lowdenslager, who collaborated with Henry Helson.

McShane died of congestive heart failure at the University of Virginia hospital.