Kress is a city in Swisher County, Texas, United States. The population was 596 at the 2020 census. Kress is located at 34°21′54″N 101°44′5…Kress is a city in Swisher County, Texas, United States. The population was 596 at the 2020 census. Kress is located at 34°21′54″N 101°44′53″W / 34.36500°N 101.74806°W. According to the United States Census Bureau, the city has a total area of 0.6 square mile, all land.