The objective of this investigation is to clarify a new and high efficient mirror machining method with using ultrasonic and low frequent vibrations, that has been named superposition superfinishing (SSFmachining). At first report, it was confirmed that stock removal could be increased by providing simultaneously 20˜50 Hz low frequent vibration and 28 kHz ultrasonic vibration on # 3000 fine abrasive stone, and that high efficient mirror machining on this new process could be practically achived. On this report, Average cutting speed and maximum cross angle can be calculated with analyzing the abrasive cutting track on superposition machining. And on the several experiments with changing rotational frequency, and vibration speed of abrasive stone, it is found that stock removal amount on this superposition superfinishing is strongly influenced by the cutting length better than the maximum cross angle, because.the maximum cross angle is constantly made large.