Eldridge was commissioned into the Royal Artillery in 1915 during World War I and served in France and Belgium.

[1] He was awarded the Military Cross in September 1917 for his actions during the war,[2] and the Distinguished Service Order in January 1919.

[1] He attended the Staff College, Camberley, alongside future general officers such as William Dimoline, Leslie Lockhart and Ashton Wade, from 1933 to 1934.

[1] He became Director General of Artillery at the Ministry of Supply in 1945 and Commandant of the Royal Military College of Science in 1948.

[1] He was made General Officer Commanding Aldershot District in 1951 and Controller of Munitions at the Ministry of Supply in 1953; he retired in 1957.