A method is disclosed, whereby a reduced wear of the polishing tool and a reduced duration for the polishing process may be achieved and also free form surfaces and non-rotating workpieces may be polished. The above may be achieved whereby the surface of the tool actually in contact with the workpiece lies off the tool axis. The invention further relates to a method for polishing a surface of a workpiece, via a tool rotating about a tool axis, whereby the workpiece, at least in one region of the workpiece surface has a contacted surface which is part region of a surface for machining, which for its part is at least part of a polishing surface of the tool, whereby the tool axis intersects the polishing surface.