A method and an apparatus for grinding the surface of a semiconductor wafer by moving a holding table (12) and a grinding wheel 4 A; 4 B; 4 C) relative to each other in a predetermined direction substantially parallel to the surface of the semiconductor wafer (W) held onto the holding table (12) to cause the grinding wheel (4 A; 4 B; 4 C) which is rotated to act on the surface of the semiconductor wafer (W) held onto the holding table (12). The semiconductor wafer (W) is placed on the holding table with its angular position being regulated so as to direct its crystal orientation in a predetermined direction with respect to the holding table (12), and thus the grinding direction of the surface of the semiconductor wafer (W) by the grinding wheel (4 A; 4 B; 4C) is set in a predetermined relationship to the crystal orientation of the semiconductor wafer. At the periphery of the semiconductor wafer (W) is formed a deformed portion (52, 54) arranged at a predetermined angular position with respect to its crystal orientation, and the holding table has a vacuum suction area made of a porous material and shaped substantially correspondingly to the shape of the semiconductor wafer.