Abstract: The forced vibration characteristic of a single Degree of freedom 1/4 hysteretic nonlinearity vehicle suspension system under multi-frequency excitation is studied by the period-energy relationship of direct two-dimensional Hamilton system and KAM theory. The theoretical analysis for eigenperiod of forced kinetic system is discussed in two initial conditions. The existence of safe quasi-period state is proven. The possibility and cause of chaos are analyzed through the Melnikov function. Numerical simulations are given separately for quasi-period and chaos state discussion. The results may supply theoretical bases for parameter recognition of the analysis and optimal design of stabilized region of vehicle suspension systems.