Plates have wide range of applications in many industries, such as the hull of ships, the pile of bridges, submarine and aerospace industries. Since plate thickness is much smaller than its typical in-plane dimension, strength design of plate structures mainly rely on buckling capacity of plates. For this reason determining the buckling capacity of plate structures is very important. On the other hand, because of production process such as rolling, plates are intrinsically anisotropic. Therefore, when buckling of a plate is to be studied, it is important to consider plastic anisotropic behavior to obtain a reliable prediction of buckling capacity of the plate structure. In this thesis elastic-plastic buckling of thick skew plate with orthotropic plastic anisotropy is studied. The plate is assumed to be under uniform edge traction, in a manner that a uniform biaxial stress state is developed in the plate. Two kinds of simply supported and clamped boundary conditions were considered and studied. The critical buckling load was determined based on minimizing the integral criterion of uniqueness of solution. For this purpose, based on the Rayleigh-Ritz method, polynomial functions were used as trial functions to approximate the transverse deflection and rotation of the plate mid-plane. Both of the Incremental and Deformation plasticity theories were utilized to determine the plastic buckling load. The uniaxial behavior of the material was modeled by the Ramberg-Osgood model, which has been widely used in previous researches. To derive elastic-plastic constitutive equations, Hill’s 48 orthotropic yield criterion was employed. Minimizing the total energy results in a homogeneous algebraic system of equation in terms of the polynomial coefficients as the unknown. For non-trivial solution, the determinant of the coefficient matrix must be equal to zero. This leads to a nonlinear algebraic equation by which, the critical buckling load is determined as the lowest root of the equation. To investigate the effect of anisotropy on buckling load, four different categories of anisotropy coefficients, along with skew angle effect, change thickness and dimensions ratio were considered. A MATLAB code was developed to determine the critical buckling load of an anisotropic skew plate. The largest relative difference in critical buckling load of an anisotropic plate, compared with similar isotropic one, was observed in uniaxial compression of a plate with a skew angle equal to 45°, the thickness-ratio of 0.1, and for simply supported boundary conditions. Keywords : Elastic-Plastic Buckling, Thick Skew Plate, Hill-48 Plastic Anisotropy, Integral Criterion of Uniqueness, Rayligh-Ritz Method.