PURPOSE: To increase a polishing quality and polishing efficiency by fixing an air cylinder for eccentricity holding in the state of being eccentric from the shaft center of a rocking drive shaft.

CONSTITUTION: When a rocking drive shaft 14 is rotated and driven in the state of the rocking projector 10 of a main body being made eccentric by an air cylinder 19 for eccentricity, a whole main body 1 is rocked. Due to the rocking projector being positioned on the axial line of a polishing main shaft 8, the polishing main shaft performs precession by the rocking and a polishing tool 9 fitting to this front end performs a circular movement. The necessary polishing action becomes fulfilled with the polishing tool being slided and moved along the work internal periphery while its revolving at high speed, by positioning the grinding tool 9 inside a tubular work W1 after setting the size of this circular motion adequately and rotating and driving the polishing main shaft and rocking drive shaft. Because of the rocking projector being held in an eccentric state by the air cylinder 19, the contact pressure of the tool becomes uniform over the whole work internal peripheral based on the air elasticity of the air cylinder proper.