The British established a Hudson's Bay Companytrading 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.
As of the census of 2010, there were 1,963 people, 770 households, and 505 families living in the city. The population density was. There were 830 housing units at an average density of. The racial makeup of the city was 97.0% White, 0.3% African American, 0.6% Native American, 0.2% Asian, 0.8% from other races, and 1.2% from two or more races. Hispanic or Latino of any race were 1.5% of the population. There were 770 households of which 37.5% had children under the age of 18 living with them, 51.9% were married couplesliving together, 8.4% had a female householder with no husband present, 5.2% had a male householder with no wife present, and 34.4% were non-families. 30.8% of all households were made up of individuals and 15% had someone living alone who was 65 years of age or older. The average household size was 2.49 and the average family size was 3.16. The median age in the city was 36.3 years. 30.4% of residents were under the age of 18; 4.9% were between the ages of 18 and 24; 25.7% were from 25 to 44; 25% were from 45 to 64; and 14% were 65 years of age or older. The gender makeup of the city was 48.0% male and 52.0% female.
2000 census
As of the census of 2000, there were 1,714 people, 682 households, and 459 families living in the city. The population density was 1,276.0 people per square mile. There were 750 housing units at an average density of 558.4 per square mile. The racial makeup of the city was 98.54% White, 0.18% African American, 0.23% Native American, 0.35% Asian, 0.18% from other races, and 0.53% from two or more races. Hispanic or Latino of any race were 0.93% of the population. There were 682 households out of which 33.6% had children under the age of 18 living with them, 56.2% were married couples living together, 7.5% had a female householder with no husband present, and 32.6% were non-families. 28.6% of all households were made up of individuals and 14.1% had someone living alone who was 65 years of age or older. The average household size was 2.43 and the average family size was 3.00. In the city, the population was spread out with 26.7% under the age of 18, 8.7% from 18 to 24, 27.8% from 25 to 44, 21.4% from 45 to 64, and 15.5% who were 65 years of age or older. The median age was 36 years. For every 100 females, there were 93.5 males. For every 100 females age 18 and over, there were 90.5 males. As of 2000 the median income for a household in the city was $41,157, and the median income for a family was $48,056. Males had a median income of $35,509 versus $22,885 for females. The per capita income for the city was $18,153. About 5.5% of families and 7.4% of the population were below the poverty line, including 8.1% of those under age 18 and 8.4% of those age 65 or over.
