A grinding method and apparatus having a position aligning mechanism to correctly achieve the centering of each work on a work table and locate an orientation flat part of each work at a predetermined position, and a displacing mechanism for reciprocally slidably displacing a top ring and the work table in order to assure that the center of each work is positionally aligned with the center of each top ring at an original position after completion of the centering of each work on the work table and the locating of the orientation flat part, and subsequently, centering each top ring with the gravitational center of each work so as to cancel a positional offset state prior to holding the work with the top ring to thrust the work against the grinding or polishing surface. The invention also includes a polishing method and apparatus in which both of a top ring and a rotary disc are reciprocally slidably displaced to improve the polishing efficiency of the device.