Abstract: A grinding machine for grinding the peripheral surface of a cylindrical workpiece having a rotatable axle extending from it by a rotating grinding roller has a feeding device which grips the axle of the workpiece and advances the workpiece against the perimeter of the grinding roller. The machine is intended for grinding ordinary spinning cylinders comprising two cylinders of hard rubber material which are rotatably mounted at a distance from each other on a common axle and particularly for regrinding such spinning cylinders, which can experience unequal wear, in order to precisely equalize their diameters.