PURPOSE: To enhance the processing accuracy in honing of the internal circumferential surface of a blind hole, in particular the accuracy of the straightness.

CONSTITUTION: Movably in the radial direction, a whetstone table 5 for honing is supported alongside the outside circumference of a cylindrical honing head body 7, and a taper cone 2b accommodate therein moves i the axial direction independently from another taper cone 1a, and thereby the stop side of the whetstone table is expanded forcedly in the radial direction with movement toward the stop side of the hole to be processed. Thus a blind hole can be processed effectively.