He received the Medal of Honor for gallantry fighting the Kiowa Indians and Chief Kicking Bird at the Battle of the Little Wichita River on July 12, 1870.

Eldridge returned to military service years later when he enlisted in the U.S. Army in Detroit and was assigned to the 6th U.S. Cavalry.

On July 6, 1870, he was among the cavalrymen under Captain Curwen B. McClelland who left Fort Richardson (near Jacksboro, Texas) to pursue renegade Indians who had seized mail from nearby Rock Station.

Despite being outnumbered and outgunned, the cavalry troopers managed to force the Kiowas to retreat after heavy fighting.

After returning to Fort Richardson, Eldridge and 12 other soldiers were received the Medal of Honor for "gallantry in action" on August 25, 1870.