PURPOSE: To absorb roughness on a non-polished surface by a soft plate and to highly accurately polish a surface to be polished by sticking a soft plate to a base plate, sticking the non-polished surface of a workpiece thereto by liquid and circumferentially laying a control ring along the outer periphery of the workpiece.

CONSTITUTION: A polishing machine is provided with a polishing plate 2 pivotally supported on one side rotary shaft 2a with polishing cloth 1 spread and a base plate 3 pivotally supported on the other side rotary shaft 3a by holding a workpiece W. The workpiece W is held between both plates 2 and 3 and polished. In such constitution, a soft plate 4 formed of a soft member is stuck to the base plate 3. The non-polished surface Wa of the workpiece W is stuck by liquid to the soft plate 4. A control ring 5 is circumferentially laid on the outer periphery of the workpiece W slightly lower than a surface Wa to be polished thereof. Thus, roughness on the non-polished surface Wa is absorbed by the soft plate 4 and the surface Wb to be polished is highly accurately polished.