The dynamic characteristics of the flexible nonlinear synchronous vibration pile system were studied. The nonlinear dynamic models of the system were proposed to analyze the nonlinear stiffness of the soil, which were induced by the relationship between the nonlinear stress and the strain in the soil. The periodic solutions of the system were investigated using Lyapunov function of the amplitude-frequency characteristic equation for the nonlinear models. The amplitude-frequency characteristics were analyzed through the selected parameters. The dynamic characteristics of the system were presented for the changes of system parameters (including the vibrating frequency, the stiffness of the soil and the damping of the soil, the radius of the eccentric block), which are induced by the amplitude-frequency characteristics. Finally, the stable solution of multiple periodic solutions can be obtained by the different initial conditions, using Runge-Kutta method. The stability of periodic solutions was theoretically analyzed by theory and verified by simulation, and the influence of different parameters on the periodic solution was presented.