Composite materials have been obtained by combining two or more material on the microscopic scale. Laminated plates are made of several individual layers. In which the fibers are oriented in a specified direction to efficiently provide required strength and stiffness parameters. Rectangular plates made of laminated composite material have been used extensively in various branches of engineering and industrial products such as building structures, aerospace, aircraft, marine and etc., due to high strength and stiffness, low weight, excellent resistance to corrosive substances and satisfactory durability under fatigue loading. To use laminated composite plates effectively and rightly a perfect understanding of their mechanical behavior under various loading with different boundary conditions is needed. These plates are often employed in situation where they are subjected to in-plane compressive loading, so buckling is very probable for them. Buckling of composite laminated plates usually generates large deformation in low stress. Thus, it can be dangerous and solving the buckling problems accurately is very important. The buckling problem of laminated composite plates has been investigated by many researchers with different methods. In the present study, the elastic stability of both isotropic and composite laminated plates with different end conditions and also the inelastic buckling of thick plates are studied by the finite layer method. The plate can be subjected to uniaxial or biaxial compression loading. The finite layer method is an extension of the well-known finite element method. This method efficiently transformed three-dimensional problem into one-dimensional because of the trigonometric properties. By using the finite layer method the transverse shear stiffness is calculated so the results can be more accurate for buckling of thick plates. In the finite layer method each lamina in the composite plate is divided by one or more finite layers. For the in-plane interpolations of displacements trigonometric functions are used that are dependent on boundary condition, while polynomials are employed in the thickness direction. By assuming the displacement functions, u, v and w and using energy approach, for each layer the stiffness and stability matrices are obtained. Then for all the layers forming the plate stiffness and stability matrices by using connectivity matrix is assembled to give an eigenvalue matrix which can be solved for the critical buckling load of the plate. Deformation theory is used for solving the inelastic buckling of the plates. Deformation theory gives more accurate results than flow theory for inelastic buckling. For the plates with high width to thickness ratio elastic buckling and for the plates with low width to thickness ratio inelastic buckling is happened. For solving the inelastic buckling of thick plates by using the finite layer method three dimensional formulations is needed. This method enables a full three-dimensional analysis, it is economical and simple to program, saves time and computing effort and also reduces storage requirement. Numerical results for elastic and inelastic buckling of plates are presented to demonstrate the accuracy and efficiency of this method. The effects of thickness, loading, aspect ratios, different boundary conditions and number of layers on buckling of plates are studied. Keywords: Finite Layer Method, Laminated Composite plate, Local buckling, Inelastic buckling