PURPOSE: To finish a workpiece with prescribed accuracy, by providing a plurality of rigid hones side by side and sequentially using the hones so that the diameter of the succeeding hone is larger than that of the preceding one.

CONSTITUTION: The workpiece 3 is mounted in a position which is set on a work head 2 not to face the hones. The work head 2 is indexed by one pitch of the hones. The workpiece 3 is placed in the face of the first hone 91 of smallest diameter. The hone is moved down by a motor 8 while rotated by another motor 10, thereby honing thw workpiece. The work head 2 is then indexed by one pitch. The workpiece is placed in the face of the second hone 92 of second smallest diameter so that the workpiece is honed. The work head 2 is indexed (n+1) times in total. The workpiece 3 is finally machined by the hone 9n of finishing diameter. The workpiece is thereafter removed from the work head 2.