When soft polymers are cut by means of a knife blade, cutting surface quality is determined by the following factors. The first is geometrical factor, i. e. the shape and the machining accuracy of the knife-blade. The second is a dynamic factor, i. e. the method of cutting and the behavior of cutting resistance. The last is a metallurgic factor, i. e. the knife-blade material and the heat treatment. In the previous reports, the above-mentioned dynamic factor was dealt with analytically and the theoretical results were confirmed by a series of experimental studies. This paper treats principally the first geometrical factor, and the relationship between the curvature radius of the blade and cutting resistance is analyzed theoretically. It is proved that the theoretical results are well agreed with the experimental results. And, the effect of the blade surface roughness is considered through some experiments. Consequently, it is clear that the cutting method with the blade vibrated sinusoidally is able to decrease cutting resistance.