The　extended　Melnikov　method　is　improved　to　investigate　the　nonautonomous　nonlinear　dynamical　system　in　Cartesian　coordinate.　The　multipulse　chaotic　dynamics　of　a　simply　supported　functionally　graded　materials　(FGM)　rectangular　plate　subjected　to　transversal　and　in-plane　excitations　is　investigated　in　this　paper　for　the　first　time.　The　formulas　of　the　FGM　rectangular　plate　are　two-degree-of-freedom　nonautonomous　nonlinear　system　with　coupling　of　nonlinear　terms　including　several　square　and　cubic　terms.　The　extended　Melnikov　method　is　improved　to　enable　us　to　analyze　directly　the　nonautonomous　nonlinear　dynamical　system　of　the　simply-supported　FGM　rectangular　plate.　The　results　obtained　here　indicate　that　multipulse　chaotic　motions　can　occur　in　the　simply-supported　FGM　rectangular　plate.　Numerical　simulation　is　also　employed　to　find　the　multipulse　chaotic　motions　of　the　simply-supported　FGM　rectangular　plate.