An abrading machine and abrading method are provided which permit a workpiece to be abraded without damage even in the case of heavy stock removal. A work holding member for mechanical abrasion includes a first holding member with a hole for receiving a workpiece and which transmits external drive force to the workpiece, and a second holding member placed on the first holding member and also having a hole for receiving the workpiece. The second holding member is removed after a predetermined volume of stock is abraded away; the workpiece is then abraded to a target thickness while being held by the first holding member alone. Thicknesses t1 and t2 of the first and second holding members are given by T1>t1+t2 and (½)T2≦t1, where T1 and T2 represent the workpiece thickness before and after abrasion, respectively.