Elbert is a census-designated place in Throckmorton County, Texas. On State Highway 79 and Farm Road 1711 in eastern Throckmorton County. In 2000, the population was 56, and in the 2020 census the population was 29. Elbert continues to serve the same community today, featuring a farm supply store, an animal feed store, a gas station, an antique store, a church, and a cemetery.