Abstract: With the help of an uncoupled approach of modal matrices, the symmetrical periodic motion and Poincaré mapping of a three-degree-of-freedom vibrating system with two rigid constrains are derived analytically. Quasi-periodic motions of the system are investigated by concerning one complex conjugate pair of eigenvalues passing through a unit circle in Jacobian matrix. In non-resonance case and three strong resonance cases, quasi-periodic motions of symmetrical periodic motions and their routes to chaos via lock phase or torus doubling are also illustrated by numerical simulation. And the excited-frequency range from quasi-periodic motions to chaotic motions of the system is obtained.