Two ships of the Royal Australian Navy have borne the name Torrens, for the Torrens River in South Australia which rises in the Mount Lofty Ranges and flows through Adelaide into the Gulf of St. Vincent.

The first HMAS Torrens (D-67) was a River class torpedo boat destroyer laid down by the Cockatoo Docks and Engineering Company Propriety Limited at Sydney in New South Wales on 25 January 1913, launched on 28 August 1915 by Lady Helen Munro-Ferguson, wife of the Governor-General and commissioned on 3 July 1916. HMAS Torrens paid off into reserve on 19 July 1920 and was based on Westernport for Royal Australian Navy Reserve Training from June 1924 to mid March 1925. During the general reduction in naval activity imposed by lack of finance during the depression it was decided to scrap the six Torpedo Boat Destroyers and she was towed to sea by the tug Heroic for use as a Fleet Gunnery Practice Target on 24 November 1930. She withstood considerable shelling before being sunk by a charge of gelignite placed in her hull.

The second HMAS Torrens (53) was a River class destroyer escort laid down by the Cockatoo Docks and Engineering Company Propriety. Limited at Sydney in New South Wales on 18 August 1965, launched on 28 September 1968 by Dame Zara Holt, DBE, and commissioned on 19 January 1971. HMAS Torrens paid off in 1998 and was sunk as a target by the submarine HMAS Waller off Western Australia on 14 June 1999.