Location in Pennington County and the state of South Dakota. Box Elder, South Dakota. Box Elder (Lakota: čhaŋšúška; box elder maple) is a city in Meade and Pennington counties in the State of South Dakota. The population was 7,800 at the 2010 census. Ellsworth Air Force Base lies on the north side of the city. Box Elder was named from nearby Boxelder Creek.