Abstract: According to the Galerkin method, the control equation of rectangular thin plates with four sides free on the Winkler foundation under harmonic excitation is translated into nonlinear vibration equations. Using the method of multiple scales of the nonlinear vibration, the first approximate solutions and corresponding steady state solutions of the three superharmonic resonance of the system are obtained. Numerical calculation is carried out. Singularities of the three superharmonic resonance solution are investigated. The transition variety and bifurcation diagram of unfolding parameter plane are obtained. Some new dynamics phenomena are pointed out.