The bifurcations of periodic solutions for a parametrically and externally excited rectangular thin plate with 1:1 internal resonance were investigated. First, the equations of motion with two degree of freedom of the rectangular thin plate were derived from the von Kármán equation and Galerkin's method. Then，based on periodic transformations and Poincaré map, the subharmonic Melnikov function was improved to analyze the periodic solutions of four dimensional non autonomous systems. Numerical simulations verified the analytical predictions.