An　analytical　approximation　is　developed　for　solving　large　amplitude　nonlinear　free　vibration　of　simply　supported　laminated　cross-ply　composite　thin　plates.　Applying　Kirchhoff＇s　hypothesis　and　the　nonlinear　von　Karman　plate　theory,　a　one-dimensional　nonlinear　second-order　ordinary　differential　equation　with　quadratic　and　cubic　nonlinearities　is　formulated　with　the　aid　of　an　energy　function.　By　imposing　Newton＇s　method　and　harmonic　balancing　to　the　linearized　governing　equation,　we　establish　the　higher-order　analytical　approximations　for　solving　the　nonlinear　differential　equation　with　odd　non-linearity.　Based　on　the　nonlinear　differential　equation　with　odd　and　even　nonlinearities,　two　new　nonlinear　differential　equations　with　odd　nonlinearity　are　introduced　for　constructing　the　analytical　approximations　to　the　nonlinear　differential　equation　with　general　nonlinearity.　The　analytical　approximations　are　mathematically　formulated　by　combining　piecewise　approximate　solutions　from　such　two　new　nonlinear　systems.　The　third-order　analytical　approximation　with　better　accuracy　is　proposed　here　and　compared　with　other　numerical　and　approximate　methods　with　respect　to　the　exact　solutions.　In　addition,　the　method　presented　herein　is　applicable　to　small　as　well　as　large　amplitude　vibrations　of　laminated　plates.　Several　examples　including　large　amplitude　nonlinear　free　vibration　of　simply　supported　laminated　cross-ply　rectangular　thin　plates　are　illustrated　and　compared　with　other　published　results　to　demonstrate　the　applicability　and　effectiveness　of　the　approach.　[DOI:10.1115/1.3142881]