A two-degree-of-freedom collission vibration system model with nonlinear constraints and initial precompression is established. The hysteresis region and distribution of the system are studied by using the 4-order Runge-Kutta numerical algorithm and multi-parameter co-simulation method. The stability of the co-existing motions in the hysteresis region is analyzed by cell mapping method. Finally, the influence of the change of basic parameters on the hysteresis domain of the system is deeply studied. The results show that the stability of coexisting motion changes with the change of excitation frequency in hysteresis domain. The decrease of the elastic stiffness ratio will reduce the hysteretic frequency of the system.