Burnside is a home rule-class city in Pulaski County, Kentucky, in the United States. The population was 611 at the 2010 census. In 2004, …Burnside is a home rule-class city in Pulaski County, Kentucky, in the United States. The population was 611 at the 2010 census. In 2004, Burnside became the only town in Pulaski County or any adjoining county to allow the sale of alcoholic beverages in qualified establishments. Since then, Burnside has annexed about eight miles of shoreline along Lake Cumberland in order to include Lee's Ford Marina on Fishing Creek, allowing it to sell alcohol.