In order to analyze the motion gait of the flexible leg rimless wheel, the conditions for the transition between the two motion states of viscosity and sliding of the flexible leg rimless wheel were analyzed. The dynamic model of the system was established through the first-order Lagrange equation.During modeling, the tangential constraint condition during the single-support phase was removed, and the friction term was added to achieve the modeling of sliding state when the friction force was insufficient. The motion gait of the flexible leg rimless wheel under different friction coefficients was analyzed, and it is found that up to four possible motion behaviors could occur. The influence of different gaits on the energy of the system was studied, and it is found that the occurrence of sliding increased the kinetic energy of the system during the single-support phase. Using NewtonRaphson iteration method and Poincare mapping, it is found that all four motion behaviors had fixed points and stable trajectories, and it is also found that the gait with sliding of the flexible leg rimless wheel had good robustness. By studying the influence of different initial kinetic energy on the system’s sliding gait, it is found that there is a very small stagnation interval when the kinetic energy or angular velocity of the system is within a certain range, which makes the single support stage of the system slide for a long time near the vertical equilibrium surface, resulting in instability of the system.