Sheldon was born in London on 6 July 1752, and was apprenticed to Henry Watson, elected in 1766 the first professor of anatomy of the Surgeons' Company.
Sheldon studied and taught anatomy at Watson's private museum in Tottenham Court Road, which was later wrecked by a mob.
He received his diploma at the Surgeons' Company on 2 November 1775, and then lectured on anatomy at Great Windmill Street school under William Hunter.
[1] Sheldon was surgeon to the General Medical Asylum in Welbeck Street, and on 18 July 1782 he was appointed professor of anatomy to the Royal Academy in succession to Hunter.
[1] In 1777 Sheldon opened a private theatre in Great Queen Street, where he taught anatomy, and pursued research.
He believed that he had discovered an easy method of catching whales with poisoned harpoons, and he made a voyage to Greenland that year to test it.
[1] Archibald Geikie in his biography of Barthélemy Faujas de Saint-Fond gives an account which may be garbled, and the Scot James Tytler has priority for British ascents, from August 1784.
[2][11] Sheldon spent time in studying the lymphatic system, an area on which William Cumberland Cruikshank also was working.