PURPOSE: To rotate a polishing container with high torque at a low speed and improve the polishing efficiency due to the friction collision by friction-pressing the polishing container filled with abrasive grains and polishing liquid to a circular ultrasonic vibrator to rotate it and driving it with ultrasonic traveling waves.

CONSTITUTION: A high-frequency power source E1 is connected between electrodes (a), (c) and electrodes (b), (d) circularly provided at the bottom of a vibrator 3, and a high-frequency power source E2 with the phase difference of 90° is connected between electrodes (f), (h) and electrodes (e), (g). Standing waves excited by an electrode group of the power sources E1, E2 are thereby overlapped to generate traveling waves rotating the circular vibrator 3. The traveling waves are expanded and amplified by notches of the vibrator 3 and vibrate a pressed polishing container 1 by friction and rotate it in the direction of the traveling waves. The vertical bending deflection vibration of the circular vibrator 3 is propagated to the container 1, the driving force by the traveling waves is efficiently transmitted to the container 1 by the friction force if the adhesive layer and coating layer of abrasives are provided on one or both of the pressing face of the bottom and the pressing face of the vibrator 3, and the liquid material filled in the container 1 can be stirred and mixed.