Abstract: In an apparatus for grinding plane, annular surfaces such as for lapping faying rings of gate valves, cylindrical grinding heads carrying grinding paper detachably adhering thereto, are mounted for free individual rotation in a rotating disk, so that by friction on the annular surface they rotate like planet wheels. The disk is detachably mounted on a spherical head on a shaft and connected thereto by a rockable diametrical entraining pin, and the shaft is connected to a driving shaft by sprocket wheels and chain.