A meshless element free Galerkin method (EFG) is presented to analyze the buckling of laminated composite plates using the classical (Kirchhoff's) plate theory (CPT) formulation. In the meshless EFG method, the moving least-squares (MLS) technique which does not satisfies the Kroneckar delta feature is used to set up the shape functions. The accuracy and the efficiency of the meshless EFG method are thus demonstrated by the numerical analysis of laminated composite plates with simply supported boundary conditions. Effects of the number of layers, ply orientations, the length-to-width ratio and modulus ratio on the dimensionless buckling loads are investigated. The results obtained by the EFG method are compared with those obtained by the CPT and the finite-element method (FEM). EFG results have good agreements with the analytical solutions. Comparison of results with the CPT as well as the FEM suggests that the meshless element free Galerkin method (EFG) yields an effective solution method for the analysis of laminated composite plates.