A finishing device includes a finishing belt, a finishing belt holding device, a first drive configured to rotationally drive a workpiece about a workpiece axis, and a second drive configured to oscillate the workpiece and the finishing belt relative to another along the workpiece axis. The finishing belt holding device has a holding section configured to hold a portion of the finishing belt. The portion has an active area configured to finish a circumferential workpiece surface. The portion extends in a plane which is vertical when referring to the direction of gravity and extends in a horizontal direction when referring to the direction of gravity and when viewing in the running direction of the finishing belt. The finishing device includes a workpiece holding device defining a workpiece holding axis which is vertical when referring to the direction of gravity.