This paper deals with nonlinear vibration of a continuum system with gaps under stationary random waves considered collision phenomena. In order to investigate this nonlinear vibration characteristic, experiments are made with an experimental apparatus consisting of a nonlinear vibration system. An analytical model of the cubic equation is proposed based on the restoring force characteristics in the maximum deflection curve. And, in the analysis, the dissipation energy is replaced with an equivalent viscous damping ratio. Moreover, the widen gap is taken into consideration in the analytical model by the original supposition method. This analytical model is used for the simulation analysis, and the results are compared with the experimental results. In the thickness is 1.6mm and width is 5mm, the simulation results and the experimental results showed similar shape from the restoring force characteristics and nearly value from the result of the R.M.S. values.