PURPOSE: To hone the inside surface of the noncircular sectional surface by feeding the pressurized medium into a hone holding part and allowing the hone on a hone holder to contact in free advance and retreat onto the noncircular inside surface of a workpiece by a prescribed pressure.

CONSTITUTION: A hone head 1 is inserted into the hole 6 on a workpiece 5 by the projection of a spindle, and the pressurized air is supplied into a hone holding part 10 from a pressurized fluid passage 9, and each grindstone holder 3 is projected in the radial direction against a spring 18, and a hone 16 is allowed to contact the noncircular inside surface 20 of the hole 6 by a prescribed pressure. The hone head 1 is rotated by a spindle in this pressurized state, and at the same time, the hone head 1 is reciprocated in the direction of the axis line of the workpiece 5, and then each hone 16 repeats projection and retreat from the hone body 2, following the inside surface 20, and the inside surface 20 can be lightly honed by a prescribed pressure. Therefore, the workpiece having the noncircular sectional shape, for example, the inside surface of the rotor housing of a rotary engine can be honed uniformly.