To eliminate the cause of grindstone crack even when a cylinder body is roughly ground while rotated at high speed and to ensure a good cylindrical grind with no damage of the cylinder body and no abnormal vibration.

This head includes a cylindrical polishing grindstone on ringlike grinding wheel 1 and a grindstone flange 2 which supports the back end of the grindstone 1 and a shank 3 which is chucked by a shank chuck means A of a grindstone polishing device. The grindstone flange 2 and the shank 3 are slidably a little to an axial direction but not rotatably engaged with each other, and a belleville spring 4 energizes the flange 2 to separate from the shank 3.