Due to wide range of industrial applications, the strength analysis of plate sand shells is a very important and interesting topic in the Mechanical Engineering field. Because of the small value of the thickness ratio (thickness to a typical in-plane dimension), buckling is a very important concept in analysis of plates and shells. If before the buckling is initiated, at least one material point of the structure experiences yielding condition, then buckling is called elastic-plastic, or sometimes briefly, plastic buckling. When plastic deformation of a structure is studied, selecting a proper yield criterion is a very important question. In the analysis of plastic deformation of most of the metals, as isotropic ductile materials with pressure independent yielding, there are two yield criteria which are widely used. These are von-Mises and Tresca yield criteria. In the previous researches, only von-Mises yield criterion was used in plastic buckling analysis of plates. To investigate the effect of yield criteria, in this thesis, elastic-plastic buckling of a thin rectangular plate is studied, based on the both von-Mises and Tresca yield criteria. The plate is under uniform biaxial tension/compression loading with different ratios. The critical buckling load was determined based on minimizing the integral criterion of uniqueness of the solution. A polynomial Rayleigh-Ritz approach was used to approximate transversal displacement of the plate. Both of von-Mises and Tresca yield criteria were employed to derive elastic-plastic constitutive equations for both Incremental and Deformation (IT and DT) plasticity theories. A Ramberg-Osgood stress-strain curve was supposed to model the uniaxial behavior of the plate. To investigate the effect of boundary conditions on the critical buckling load, different combinations of free, simply supported and clamped boundary conditions was examined for different edges of the plate. Substituting the increment of stress and strain components in terms of trial transverse displacement, in uniqueness criterion, the integral can be computed as a function of unknown coefficients. The result of the integral should be then minimized with respect to the unknown coefficients, appeared in the trial polynomial function. This procedure results in a homogeneous system of algebraic in terms of the unknown coefficients. For non-trivial solution, the determinant of the coefficient matrix should be equated to zero. The critical buckling load is then determined as the lowest root of the matrix determinant. A MTLAB code has been developed to derive the matrix determinant and solve for critical buckling load. To validate the analysis, critical buckling load for a simply supported square plate, under uniaxial and equi-biaxial compression, using von-Mises yield criterion, were compared with previously published results. A very close agreement was observed. Then, for the loading conditions associated with the corners, the effect of different normal vector to the yield Tresca surface, on the critical buckling load, was studied. The results show that different critical buckling load is predicted by different normal vectors. A mean normal vector has been proposed for the corner loading conditions. The results indicate that a smaller critical buckling load is predicted if Tresca yield criterion is used instead of von-Mises. Keywords: Elastic-plastic buckling, Thin rectangular plate, Tresca criterion, Ritz method