Mount Vernon is a home rule-class city and the seat of Rockcastle County in southeastern Kentucky. The intersection of U.S. Routes 25 and 15…Mount Vernon is a home rule-class city and the seat of Rockcastle County in southeastern Kentucky. The intersection of U.S. Routes 25 and 150 is located here. The population was 2,477 at the time of the 2010 U.S. census. Mount Vernon is part of the Richmond-Berea micropolitan area.