Glen Alpine is a town in Burke County, North Carolina, United States. The population was 1,517 at the 2010 census. It is part of the Hickory–Lenoir–Morganton Metropolitan Statistical Area. Glen Alpine is located in western Burke County. It is bordered to the southeast by an extension of the city of Morganton. U.S. Route 70 passes through th…Glen Alpine is a town in Burke County, North Carolina, United States. The population was 1,517 at the 2010 census. It is part of the Hickory–Lenoir–Morganton Metropolitan Statistical Area. Glen Alpine is located in western Burke County. It is bordered to the southeast by an extension of the city of Morganton. U.S. Route 70 passes through the town as Main Street, and Interstate 40 passes to the south of the town, with access from exits 98 and 100. Via US-70, it is 5 miles east to downtown Morganton and 15 miles west to Marion.