A new type of continuous kneader reactor with capability of self-cleaning, compulsory transportation, and mixture as well as plasticizing for high viscosity material mixing and malaxating is proposed in this article. Geometric analysis, optimization, and tooth profiling of the kneader reactor are described in detail and the working principles of the kneader are analyzed. The theories of profiles designing and mathematical model of the kneader are established based on gear engagement theory. The design parameters of the kneader are analyzed and the variable proportions of volumetric efficiency Cn are investigated when distance A and ratio Imf changes. The study reveals that when the profiles of female and male rotor are cycloids, the best transportation and self-cleaning ability are obtained. The analytical expression of optimal distance A is deduced with consideration of shear performance. The analytical expression of the screw rotor profiles and practical examples as well as the machining method are also presented.