Many Literatures pay attention to the location and parameter optimization of Tuned Mass Damper (TMD). Yet there are few studies on the case where both the TMD and the main system have plastic impacts under large stroke of TMD fixed in limitation space. A two degree-of-freedom (DOF) vibratory system having symmetrically placed rigid stops and subjected to periodic excitation is considered in this paper. The equations of the vibratory system are constructed, and then for simplification the dimensionless equations are obtained. Poincaré map was used to study the relationship between the motion stability and parameters. Period-doubling bifurcation of motion was found by numerical simulations. With the gradual change in excitation frequency, the routes of quasi-periodic impact motions to chaos are observed from simulation results.