PURPOSE: To make the peripheral edge part of a wafer polishable without giving it any damage such as a crack or the like, by making a degree of pressurizing force against a lapping surface plate adjustable according to increase or decrease in a speed of revolution in the lapping surface plate, in case of polishing a fragile material.

CONSTITUTION: Dispersing abrasive grains 21 wide over a lapping surface plate 1, a holder body 11 stuck on with a wafer 12 is mounted on the lapping surface plate 1 and loaded with its own weight. Then, the surface plate 1 is accelerated in speed by degrees and a revolution signal SA by a detector 5 is inputted into an operation control part 20. On the other hand, a turning amount signal SC of a valve on-off mechanism 18 by a detector 19 is also inputted in the control part, then such a control signal SB as being congruous with these signals SC and SA is given to the valve on-off mechanism 18, opening a flow regulating valve 16 according to the revolution signal SA and feeding a pneumatic cylinder 13 with air out of an air source 17, and the surface plate 1 is forcibly pressed according to the revolution speed of the wafer 12 after adding pressing force by the cylinder 13 to the dead load of the holder body 11. Thus, in time of a start or an end of machining, a sudden impact due to free abrasive grains is no longer received and damages such as cracking and/or chipping are in no case given to a peripheral edge part of the wafer.