William Stockdale was born at Skelton in Guisborough, England, on 30 November 1886. He enlisted with the Australian Imperial Force on 20 August 1914 at the age of 27. Stockdale joined the First Divisional Train of the Australian Army Service Corps (AASC) and was initially allocated the role of driver. He left Melbourne aboard HMAT Benalla on 19 October 1914.

The following year he was sent to Gallipoli, where he described in his diary the preparations for the landing and the landing itself, and detailed his own critiques of the campaign. In April 1916 Stockdale arrived on the Western Front, continuing the work of the AASC in the transport and provision of supplies and rations, including the delivery of mail to the troops. He was transferred to the Third Divisional Train of the AASC in August, and in November was promoted to the rank of lieutenant. Stockdale was transferred to the 1st Australian Depot Unit of Supply (ADUS) in June 1917 and then to the 4th ADUS in September. The following year, on 19 August 1918, he married Eleanor while on leave in the UK. Stockdale had taken leave there at least once a year since 1916 and had developed the relationship during that time. He returned to the front in mid-September and served until the end of the war. Stockdale originally applied to be discharged in the UK on the grounds that his wife lived there and he had arranged to be a partner in a business undertaking in England. When the business deal fell through he cancelled his application and returned to Australia at the end of 1919. Eleanor immigrated to Australia and the couple based themselves in Malvern, Victoria.

Stockdale once again enlisted for service in the Second World War, this time on the home front as the officer commanding the base supply depot in Melbourne and as Secretary of the Meat Canning Committee. William Stockdale died at Chatswood, New South Wales, on 27 July 1975.