A three degree-of-freedom vibro impact system with symmetric constraining stops is considered. The Poincaré map of the system is established, and the symmetry of the Poincaré map is derived in detail. The theory of bifurcation of fixed points is applied to such model, and it is shown that the symmetry of the Poincaré map suppresses codimension 1 period doubling bifurcation, Hopf flip bifurcation and pitchfork flip bifurcation of symmetric period n-2 motions. It is also proved that both the two antisymmetric period n-2 motions have the same stability. By numerical simulations, pitchfork bifurcation, Hopf bifurcation and Hopf Hopf bifurcation of symmetric period n-2 motions are represented.Besides,the routes to chaos after pitchfork bifurcation are studied in the forms of the phase portrait in the projected Poincaré section.
