In this thesis, elastic-plastic symmetrical buckling of a FGM circular plate under uniform radial compression has been investigated. To this end, a MAPLE computer code has been developed. A metal-metal type has been assumed for the FG plate. Commercial aluminum and ST1403 steel were chosen as the special case study. The mechanical properties of the plate, including elasticity modulus, density and Ramberg-Osgood parameters were assumed to vary according to a power-law function through the thickness. To minimize the integral criterion of stability, based on Rayleigh-Ritz method, transversal displacement and rotation angle were approximated by trigonometric trial function which includes some unknown coefficients and satisfies geometric boundary conditions. Substituting the trial function in the stability criterion and minimizing with respect to the unknown coefficients results in a homogeneous algebraic set of equations in terms of unknown coefficients. For non-trivial solution, the determinant of coefficient matrix should be equated to zero. Using this equation, critical buckling load is determined. The results of present study were compared with existing analytical solutions for homogenous circular plate and a good agreement was observed. The critical buckling load was calculated based on both incremental theory (IT) and deformation theory (DT), using thin plate as well as thick plate assumptions. The effect of boundary condition type, FGM power index and plate thickness on the critical elastic-plastic buckling load has been investigated. Results show that increasing the thickness-to-radius ratio and decreasing FGM power index in volume fraction lead to increasing elastic-plastic critical buckling load. Also, for simply supported boundary condition, a very small difference (less than %2) between IT and DT was observed. Keywords: Functionally graded material, elastic-plastic symmetrical buckling, circular plate, Rayleigh-Ritz method.