In this paper we propose an analytical model of the nonlinear spring in the nonlinear vibration system with gaps used by elasto-plasticity solid model and an analytical evaluation model of the nonlinear vibration characteirstics by the nonlinear spring model of a cubic equation. The results by the analytical evaluation model used self-natural frequency curve of the nonlinear vibration characteristics under sinusoidal waves are compared with the results of the simulation analysis and the experiments under random waves used by wavelet analysis. The relation betwene the displacement and the domainant frequency are changing in curve. The nonlinear vibration characteristics used the analytical evaluation model are agreed with the simulations and the experiments. The restoring force characterisktics by the analysis are agreed with the results of the experiments. The restoring force characteristics by the analysis are descirbed by the cubic equations.
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