Elk City is a city in Montgomery County, Kansas, United States, along the Elk River. As of the 2020 census, the population of the city was 260. …Elk City is a city in Montgomery County, Kansas, United States, along the Elk River. As of the 2020 census, the population of the city was 260. Elk City had its start in the year 1868 by the building of a trading post at that location. The first post office in Elk City was established in November 1869.