At the end of this dissertation we have paid attention to the analysis of post buckling behavior of circular homogenous plates with simply supported and clamped out-of-plane boundary conditions, under the effects of symmetric and asymmetric loading using Rayleigh – Ritz method. The process of action is so that first by formulating the problem in polar coordinate system we will deal with the development of differential equations governing the behavior of the plate in large deflections using Van – Karman nonlinear theory. Then using the correct and useful mapping, we will mention the geometry in natural coordinate system. Then we will deal with the development of displacement fields in natural coordinate system using Hierarchic, Hermitian and Furie series shape functions in interpolation of out-of-plane displacement field and Furie series and Lagrange shape functions in interpolation of in-plane displacement field of plates. And finally we will deal with the presentation of a proper Hookian displacement field for controlling post buckling behavior of circular plates. It should mentioned that in a circular plate with a non-centered hole, because of asymmetry in geometry we need to in-plate solution to find the distribution of stress which results in providing a support in plate and computing boundary integration that will be discussed completely afterwards. Although the main direction in this dissertation is to investigate the post buckling behavior of plates, but because of the need for the process of analyzing non-linearity we are committed to analyze stability, the formulation is so that it will be able to analyze the plate in static and buckling conditions, different results are presented in this regard.