There are many industrial applications such as aircrafts, bridges, ships and offshore structures which involve the use of plates. Due to relatively small value of thickness-to-length ratio of plates, buckling prevention is often the most important criterion in designing plate structures. Therefore, it is very important to predict the buckling load of a plate structure. Since plates are inherently anisotropic, studying the effect of anisotropy on the buckling load is also important. In this thesis, elastic-plastic buckling of a thin rectangular anisotropic plate is studied. Uniform edge compressive/tensile traction with different loading ratios has been studied. Three different types of boundary conditions, including , SCSC and CFCF, have been considered. The material has been assumed to obey Romberg-Osgood model in uniaxial tension. Both of the two conventional plasticity theories, Deformation Theory (DT) and Incremental Theory (IT), have been used to predict the buckling load. Elastic-Plastic constitutive equations for both the DT and IT theories have been developed based on Hill’s (1948) orthotropic yield criterion. The integral uniqueness criterion has been minimized to determine the critical buckling load. For this purpose, a polynomial-form trial function has been employed to approximate the transverse displacement of the plate. Next, the total potential energy has been minimized with respect to the unknown coefficients of the trial function. This results in a homogeneous system of equations in terms of the unknown coefficients. For nontrivial solution, the determinant of the coefficient matrix should be vanished. The critical buckling load has been then calculated using the lowest eigenvalue of the coefficient matrix. Aluminum AL 2024 T3 has been considered as the case study. Convergence of the results has been investigated to show that a proper polynomial with adequate terms has been selected to approximate the transverse displacement. To verify the present results, the critical buckling load for an isotropic rectangular thin plate has been calculated which was in a good agreement with similar previously published results. The effect of loading ratio and boundary conditions on the buckling load of an anisotropic plate was investigated based on both the plasticity theories. Neglecting the effect of anisotropy, a maximum difference of 10% in the buckling load was found compared with that when anisotropy is considered which means the effect of anisotropy on the buckling load is not considerable. Keywords: Elastic-Plastic Buckling, Thin Rectangular Plate, Orthotropic Hill’s 48 Yield Criterion, Ritz Method.