Heaps is a surname. Notable people with the surname include:
Abraham Albert Heaps (1885–1954), Canadian politician and labor leader
Adrian Heaps (born c. 1954), Canadian politician
Elizabeth Heaps, English academic and archivist
Jake Heaps (born 1991), American football player
Jay Heaps (born 1976), American soccer player
Stanley Heaps (1880–1962), English architect