The mechanical model of flexspline gear ring was theoretically established aiming at the design demand of flexspline such as small size, high stiffness and long life. The matching and compensating method of dimension was explored in the design. Then the finite element analysis was conducted in ANSYS Workbench by using response surface method and central composite design (CCD) method, and the response surface of stress and stiffness was analyzed. The influence law of each structural parameter on stress and stiffness were obtained. The analysis results show that radial deformation can be reduced to counteract the increased stress when radius decreases, and thickness can be reduced to counteract the generated stress when length decreases in the design of small volume. The small volume design of the flexspline will weaken the bearing capacity and aggravate the phenomenon of stress concentration and fatigue damage at the ring gear. It is necessary to increase the ratio of thickness to diameter or reduce the radial deformation to reduce the phenomenon of stress concentration at the end of the ring gear under the condition of ensuring the meshing state and the bearing capacity. The regression curves of stress and stiffness were obtained, which can be used to obtain optimal value.