This paper presents the motion principle, mechanical modeling, and key characteristics of the propulsion force of a new flexible fin traveling wave propulsion mechanism used in an amphibious robot. Firstly, the form of motion and the basic propulsion principle of traveling wave propulsion of flexible fins on the ground are described. During the fluctuation of the flexible fins, the relative motion between the outermost contact line of the fin surface and the ground generates the propulsive force of forwarding motion and the lateral force along the fin surface. Based on the laws of flexible fin fluctuation kinematics and the basic principles of friction mechanics, the propulsion mechanics model of flexible fins during traveling wave propulsion on the ground is established. By numerically solving the propulsive force equation, the relationship between the propulsive force of the flexible fin and the motion parameters of the fin surface can be obtained. Numerical calculations combined with experimental test results reveal that the flexible fin propulsion force shows periodic variations within one fluctuation period of the fin surface, and the variation period is related to the number of waves present in the fin surface. The number of waves on the fin surface has a large impact on the fluctuation amplitude of the propulsion force. In the range of 1.6-1.9 waves on the fin surface, the average propulsion force is most ideal, while in the range of fin surface inclination less than 50° and fluctuation amplitude greater than 30°, the propulsion force of the flexible fin is the ideal parameter range. This research provides theoretical support for the design of flexible fins traveling wave propulsion mechanism.