Nowadays, plates and shells are widely used in various engineering applications such as shipbuilding, bridges and aerospace industries. Plates are usually under in-plane uniaxial or biaxial compressive edge traction which may result in buckling failure. Therefore, studying the buckling capacity or buckling strength of plates is one of the most important subjects in the designing procedure of a plate-structure. On the other hand, the plates which are produced by cold rolling process are inherently anisotropic due to preferred orientation or mechanical fibering, which in turn may be resulted from the alignment of any impurities. Henceforth, it is a natural question that how does the anisotropy characteristics affects the buckling capacity of a plate structure. The present thesis aims at the investigation of elastic-plastic buckling of a rectangular orthotropic thick plate, with variable thickness, under uniform uniaxial or biaxial compressive edge traction. Two types of simply supported and clamped boundary conditions were considered for the plate edges. In order to model the plastic behavior of plate, both of the incremental and deformation plasticity theories were used. Also, the most novelty of this study was the change in the thickness of the plate according to the length of it, so that thickness changes as a linear function of length .Ramberg-Osgood equation was assumed for the uniaxial stress-strain curve of plate to obtain material constants. The critical buckling traction was determined based on the integral criterion of uniqueness of solution. To this end, polynomial Rayleigh-Ritz method was used to approximate the transversal deflection and rotations degrees of freedom of plate. Substituting the approximate functions into the integral criterion and then, minimizing the integral in terms of the polynomial unknown coefficients results in a homogeneous system of equations. In order to obtain the non-trivial solution, the determinant of the matrix of the coefficients should be equal to zero. Therefore, a nonlinear algebraic equation is obtained. The critical buckling traction is calculated as the lowest root of the equation. In order to verify the analysis, it was shown that as the polynomial order is increased, the results are converged. Then, the critical buckling load for a thick isotropic rectangular plate with uniform thickness, under equi-biaxial loading and simply supported boundary conditions, were calculated and compared with previously published results. A very close agreement was observed which evidently shows the validity of the analyses. Finally, the effect of anisotropic coefficients, the slope of thickness variation and the aspect ratio of the plate on the critical buckling load was studied. Keywords : Elastic-Plastic Buckling, Rectangular Plate, Hill-48 Plastic Anisotropy, Variable Thickness, Strength and Potential Energy, Rayligh-Ritz Method