Circular and annular plates are used in turbine disks, submarines, instrument mounting bases for space vehicles and micro-electro-mechanical systems (MEMS) devices. When these circular and annular plates are used in the applications in which, in-plane compressive loads are applied, the buckling capacity needs to be determined. In this thesis, elastic-plastic buckling of a thick solid circular plate with orthotropic anisotropy, under uniform edge pressure is investigated, based on both Incremental Theory (IT) and Deformation (DT) plasticity theories. Two kinds of simply supported and clamped boundary conditions have been considered. To minimize the integral uniqueness criterion, based on Rayleigh-Ritz method, transversal displacement and rotations about the ?? and ?? axes, were approximated by polynomial test functions, which includes some unknown coefficients and satisfies geometric boundary conditions. Substituting the test functions in the stability criterion and minimizing with respect to the unknown coefficients results in a homogeneous algebraic set of equations in terms of the unknown coefficients. For non-trivial solution, the determinant of the coefficient matrix should be equated to zero. Using this equation, critical buckling load is determined as the lowest rot of the equation. To verify the present results, the critical buckling load for an isotropic circular thick plate was calculated and compared with the similar previously published researches. A very good agreement was observed which evidently shows the validity of the presented analysis. Then, the Al 2024-T3 was selected as the case study to investigate the effect of anisotropy on the critical buckling load. The results show that for an anisotropic plate the critical buckling load may reduce up to 12% compared with a similar isotropic plate. Keywords Elastic-Plastic Buckling, Thick Circular Plate, Hill-48 Plastic Anisotropy, Integral Criterion of Uniqueness, Rayligh-Ritz Method.