A Pilates step barrel/chair exercise apparatus has side walls and a unique elastic resistance member anchor structure fastened to each of the side walls. Each anchor structure has an anchor socket assembly fastened to one of the side walls and a removable elastic member anchor bar assembly mounted in the anchor socket assembly. The anchor socket assembly has a central tubular portion passing through the one of the side walls and a flange portion fastening the tubular portion to the side wall. The anchor bar assembly has an L shaped anchor bar, a cylindrical yoke receiving and holding a long leg of the anchor bar, and a spring bar tube rotatably fastened to a short leg of the anchor bar. The cylindrical yoke has a portion adapted to fit within a central bore of the tubular portion of the anchor socket assembly, and has a plurality of spaced radial holes therearound for engaging with and retain the anchor bar assembly in the anchor socket assembly.