W.K. Eltham was born and grew up in Hobart. He was educated at Queens College, Hobart, and later worked as a clerk/draftsman at the City Engineer's Department. He was a keen athlete and sportsman, and represented Tasmania at cricket, playing eleven first class matches in the period 1909-1914. He also had artistic interests, and in the years prior to World War I was involved in a number of Hobart amateur theatrical productions. He also evidently contributed cartoons and sketches to several Australian newspapers.
During World War I, Eltham served in the AIF, initially as a gunner in the 9th Field Artillery Brigade and later as a lieutenant in the 1st Field Artillery Brigade. He served at Gallipoli (where he was wounded) and subsequently on the Western Front. He was killed by artillery fire near the village of Flers, in northern France, on 31 December, 1916.
Two of Eltham's sketches, 'North Flank - Suvla from Anzac' and 'South Flank, Gaba Tepe from Anzac', appeared in The Anzac Book. His poem 'To the Pongo' was one of numerous 'rejects' submitted to The Anzac Book editor Charles Bean, who in 1916 found a place for it in the soldiers' magazine The Rising Sun.