The state highway heads east along Washington Avenue to the town limit of Vinton at Wolf Creek. SR 24 has an interchange with the Blue Ridge Parkway at a low gap in the Blue Ridge Mountains between Stewart Knob and Chestnut Mountain immediately before the highway enters Bedford County, where its name changes to Stewartsville Road.
The state highway follows Washington Avenue to Vinton's town limit at Wolf Creek. SR 24 connects to the Blue Ridge Parkway at a gap in the mountains between Stewart Knob and Chestnut Mountain before entering Bedford County, where its name changes to Stewartsville Road.