Abstract: A device for precision grinding and polishing the surfaces of a workpiece such as the surfaces of molds or the like includes a base means on which the workpiece is movable in one plane. A stand supported on the base plate is provided with a carrying arm on which there is mounted an oscillating device operable to oscillate a tool. The carrying arm is arranged such that it may be adjustable in all three spacial coordinates. The oscillating tool serves as the carrier for the grinding medium for grinding and polishing a workpiece disposed on the base means.