An accurately conditioned lapping plate rotates in the horizontal plane, on which conditioning rings, also rotating freely in the direction of the lapping plate, carry the work pieces, with the surface to be lapped, in contact with the lapping plate. Suitably mixed lapping compound is fed onto the lapping plate which laps/polishes the surface to be lapped and the flatness of the lapping plate is transferred to the workpiece. Lapping plate dia from 300mm to 1500mm available.