William Maxwell Simmers (7 August 1904, Glasgow - 14 November 1972, 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.