In　this　paper,　the　bifurcations　of　subharmonic　orbits　for　a　four-dimensional　rectangular　thin　plate　with　parametrically　and　externally　excitations　is　considered　for　the　first　time.　The　formulas　of　the　rectangular　thin　plate　are　derived　by　using　the　von　Karman-type　equation,　the　Reddy＇s　third-order　shear　deformation　plate　theory　and　the　Galerkin＇s　approach.　The　unperturbed　system　is　composed　of　two　independent　planar　Hamiltonian　systems　such　that　the　unperturbed　system　has　a　family　of　periodic　orbits.　The　problem　addressed　here　is　the　determination　of　sufficient　conditions　for　some　of　the　periodic　orbits　to　generate　subharmonic　orbits　after　periodic　perturbations.　Thus,　based　on　periodic　transformations　and　Poincare　map　the　subharmonic　Melnikov　method　is　improved　to　enable　us　to　analyze　directly　the　non-autonomous　nonlinear　dynamical　system,　which　is　applied　to　the　non-autonomous　governing　equations　of　motion　for　the　parametrically　and　externally　excited　rectangular　thin　plate.　The　results　obtained　here　indicate　that　subharmonic　motions　can　occur　in　the　rectangular　thin　plate.　The　method　succeeds　in　establishing　the　existence　of　subharmonics　in　perturbed　Hamiltonian　systems　as　well　as　in　discussing　their　bifurcations.　Numerical　simulation　is　also　employed　to　find　the　subharmonic　motions　of　the　parametrically　and　externally　excited　rectangular　thin　plate.