An elliptical vibratory cutting apparatus includes a control mechanism (15) which applies a sinusoidal voltage having a predetermined phase difference to piezoelectric elements (12 (14)). Flexure vibrations are accordingly generated in X and Y directions. An amount of interference, caused by vibrations in one direction, with vibrations in another direction, is correctively eliminated by the control mechanism (15) (interference eliminating unit 22). A workpiece (1) is thus cut by means of a cutting tool (2) through elliptical vibrations. <IMAGE>
