Elk Point is a city in and the county seat of Union County, South Dakota, United States. The population was 2,149 as of the 2020 census. The …Elk Point is a city in and the county seat of Union County, South Dakota, United States. The population was 2,149 as of the 2020 census. The British established a Hudson's Bay Company trading post in 1755 near present-day Elk Point. Elk Point was so named on account of the abundant elk in the area. The town was incorporated in 1873.