The disclosure relates to a finishing apparatus for finish machining of rotationally symmetric workpiece surfaces having a finish belt guide which has a guiding body for guiding the finish belt, wherein the guiding body comprises a shell-like guiding surface along which the finish belt can be guided or is guided between an insertion end of the finish belt and a withdrawal end of the finish belt, wherein the guiding surface is mounted in a resiliently elastic manner in the radial direction, wherein, when seen in the circumferential direction, the guiding surface extends in a continuous manner between the insertion end of the finish belt and the withdrawal end of the finish belt over at least a part of the width of said guiding surface and is mounted in a resiliently elastic manner.