In the previous reports, theoretical results about cutting resistance of cutting surface were considered through experiments. In the experiments soft polymers were cut by applying low frequency harmonic vibration to a knife-blade in the longitudinal direction (X direction). The present paper treats the method of elliptical vibration cutting which utilizes effective reduction of both the solid friction and the cutting resistance which occur in the cutting and non-cutting processes in one cycle of vibration. In this method, it is clear that not only is the cutting resistance in the V direction less than half of the previous results, but also the cutting resistance in the X direction has an equivalent nagative value. And in addition, the cutting surface of elliptical vibration cutting is as high in quality as in rectilinear vibration cutting. That the theoretical results agree well with the experimental results has been confirmed.