Allan Burns (18 September 1781 – 22 June 1813) was a Scottish surgeon and physician. A lecturer on surgery and anatomy at Glasgow, he studied medicine in Glasgow. He visited Russia in 1804 and he published anatomical treatises. He was the son of Revd Dr John Burns, a minister of the Barony Church, and Elizabeth Stevenson. Of his brothers, Dr John Burns (1775–1850) became Regius Professor of Surgery at the University of Glasgow; James was a shipowner and George was his partner in .