Abstract: This specification discloses a Dual Surface Lapping Machine having at least one fixed lower spindle and an upper spindle carried by an A-frame mounted on guide ways. The spindles and guide ways are parallel to one another to permit accurate lapping of piece parts and to facilitate dressing of the lapping surfaces. The upper spindle is mounted in self aligning bearing means which permits floating movement of the upper lapping surface upon work pieces of different thicknesses. To provide accurate dressing of the lapping surfaces locking means are provided to lock the self-aligning bearing. Each spindle is adapted to receive a dressing tool so as to accommodate accurate dressing of the surfaces in a manner eliminating bending deflections associated with prior art devices.