Abstract: The workpiece which is moved relative to the tool is processed by a tool configured in the form of a flexible membrane. On the rearward side of the membrane, loading units are arranged with the force of each unit being individually controlled. The pressure distribution exerted by the loading units on the workpiece is varied with time in dependence upon the position of the workpiece. With the method, large optical components such as telescope mirrors and grazing-incidence optical elements for x-ray telescopes can be polished more quickly than by the heretofore known methods. Also non-rotationally symmetrical defects of the surface can be eliminated. An apparatus for carrying out the method of the invention is disclosed.