Elephant Butte is an exposed volcanic plug in Sierra County, New Mexico. The sides of the volcano have eroded away and left only the solidified butte-shaped core. It is now an island in the lake except at low-water levels, when it is connected to land by an isthmus. The butte was said to have the shape of an elephant lying on its side, and its name has been applied to the area since before the dam's construction. The nearby city of Elephant Butte was named for the rock formation.