Eubank is a home rule-class city in Pulaski and Lincoln counties in southern Kentucky. The population was 319 at the 2010 census. Th…Eubank is a home rule-class city in Pulaski and Lincoln counties in southern Kentucky. The population was 319 at the 2010 census. The Pulaski County portion of Eubank is part of the Somerset Micropolitan Statistical Area, while the Lincoln County portion is part of the Danville Micropolitan Statistical Area.