A static load analysis of twin-screw kneaders is required not only for the dynamic analysis, but also because it is the basis of the stiffness and strength calculations that are essential for the design of bearings. In this paper, the static loads of twin-screw kneaders are analyzed, and a mathematical model of the force and torque moments is presented using a numerical integration method based on differential geometry theory. The calculations of the force and torque moments of the twin-screw kneader are given. The results show that the $M_x$ and $M_y$ components of the fluid resistance torque of the rotors change periodically in each rotation cycle, but the $M_z$ component remains constant. The axis forces $F_z$ in the female and male rotors are also constant. The static load calculated by the proposed method tends to be conservative compared to traditional methods. The proposed method not only meets the static load analysis requirements for twin-screw kneaders, but can also be used as a static load analysis method for screw pumps and screw compressors.