In older to finish an external surface of a cohntn or cylinder wcrkpiece, which does not have any clamping device, centerless roller bumishing equipment (planetary roller type) was newly proposed, and it has been practically confirmed that it can work effectively to burnish the surface of workpieces. The main part of the equipmet consists of cylindrical fixed head, rollers and hollow cylindrical frame. The assembled construction is, several rollers, which are rotatable respectively, are being supported within slots of the frame, and are deflected to the axis of the head with feed angle, and are disposed to contact an inner surface of head. By rotating frame, rollers can burnish a surface of column or cylinder when it is being passed through the equipment because of the self-propelling force by the feed angle function.