Resonant　chaotic　motions　of　a　simply　supported　rectangular　thin　plate　with　parametrically　and　externally　excitations　are　analyzed　using　exponential　dichotomies　and　an　averaging　procedure　for　the　first　time.　The　formulas　of　the　rectangular　thin　plate　are　derived　by　a　von　Karman　type　equation　and　the　Galerkin＇s　approach.　The　critical　condition　to　predict　the　onset　of　chaotic　motions　for　the　full　system　is　obtained　by　developing　a　Melnikov　function　containing　terms　from　the　non-hyperbolic　mode.　We　prove　that　the　non-hyperbolic　mode　of　the　thin　plate　does　not　affect　the　critical　condition　for　the　occurrence　of　chaotic　motions　in　the　resonant　case.　Simulations　also　show　that　the　chaotic　motions　of　the　hyperbolic　subsystem　are　shadowed　by　the　chaotic　motions　for　the　full　system　of　the　rectangular　thin　plate.