A surface grinding machine for a sintered rare earth magnetic alloy wafer comprises a pair of disk-shaped grindstones that face each other across a prescribed gap to be rotatable in opposite directions about their center axes. The grinding surfaces of the pair of grindstones and the center axe inclination of one grinding stone are configured to form a planar grinding region A wherein a portion of both of the grinding surfaces of the pair of grindstones lie parallel with a constant intervening gap therebetween. Other portions of the grinding surfaces of the grindstones constitute a wedge-like opening region B that becomes more narrow toward the planar grinding surface A. A feeder to feed the wafers from the wedge-like opening region B toward the planar grinding region A is provided in order to grind both surfaces of the wafers at the planar grinding.