As the research object,the finite element model of a certain type of RV reducer is established in a finite software,considering the meshing stiffness of planetary gears and cycloid gears,elasticity of components and the bearing stiffness. Based on the isometric and shift modification to the cycloid gears,the torsional stiffness of the RV reducer with deformation caused by the meshing force is calculated. At the same time,compare with the data obtained from experiments of torsional stiffness,it is concluded that the maximum torsional stiffness is 278. 8 N·m/（ ’）,and the minimum torsional stiffness is 247. 1 N·m/（ ’）,but the average value of torsional stiffness is larger than the experimental value by 10. 85%,the hysteresis is smaller than that by8. 9%. It shows that the finite element method is can be used for reference to simulate and analyze the torsional stiffness and the hysteresis.