This　paper　focus　on　the　nonlinear　numerical　analysis　for　an　extruding　cantilever　laminated　composite　plates　subjected　to　transversal　and　in-plane　excitation.　Based　on　the　ReddyaˆTMs　shear　deformable　plate　theory,　the　nonlinear　partial　differential　equations　of　motion　were　established　by　using　the　Hamilton　Principal.　And　then,　after　choosing　suitable　vibration　mode-shape　functions,　the　Galerkin　method　was　used　to　reduce　the　governing　partial　differential　equations　to　a　two-degree-of-freedom　nonlinear　ordinary　differential　equation.　Finally,　we　numerical　solved　the　nonlinear　ordinary　differential　equation,　and　analyzed　the　influences　of　varying　extruding　speeds　and　thickness　of　plates　on　the　stability　of　the　plates.　Copyright　©　2012　by　ASME.