Abstarct: In this thesis, the asymmetric buckling analysis of homogeneous and isotropic circular/annular plates under radial load has been performed with the first-order shear deformation theory. The buckling load has been presented for different combinations of free, clamp and simply supported boundary conditions at the plate outer edges and different aspect ratio. The equilibrium equations have been extracted using the principle of virtual work, which include five coupled non-homogeneous and nonlinear partial differential equations. The stability equations have been obtained by the adjacent equilibrium criterion, which include five coupled homogeneous linear partial differential equations with variable coefficients. The equilibrium equations have been solved analytically and the stability equations have been solved by the numerical methods. In the analytical solution, the perturbation theory has been used. In numerical solution of stability, the quadrature differential method has been used to find the eigenvalue of the system of coupled linear equations with variable coefficients. The effect of geometrical parameters on the buckling load has been investigated too. The results of the other references in special cases and numerical solution by using the finite element have been used to validate the results.