This paper studied the nonlinear vibration of FGM plate with two simply supported opposite and two free edges subjected to the inplane and transversal excitations. The geometrical nonlinear system, whose material properties of the FGM plate are assumed to be temperature dependent, was used. The resonant case considered here is 1:1 internal resonance and principal parametric resonance1/2 subharmonic resonance. The asymptotic perturbation method was utilized to obtain fourdimensional nonlinear averaged equation. Numerical method was used to find the nonlinear dynamic responses of the FGM rectangular plate. It is found that there exist periodic, quasiperiodic solutions and chaotic motions for the plates under certain conditions. It is thought that the forcing excitations can change the form of motions for the FGM rectangular plate. It is also found from the numerical simulations that the amplitude of the first mode for the FGM plate is much less than that of the second mode in the given parameters. It means that we must consider the second mode when the internal resonance occurs.