William Maxwell Simmers (7 August 1904 in Glasgow – 14 November 1972 in Helensburgh) was a Scottish rugby union player.
He was often referred to as "Max" and/or "Bill".He was capped twenty eight times between 1926–32 for Scotland, scoring six tries.
He also played for Glasgow Academicals.He was the father of Brian Simmers, who was also capped for Scotland.He married the English tennis player Gwen Sterry on 9 July 1932 at St Mark's Church, Surbiton.