Abstarct: In this dissertation, an analytical method is presented to evaluate the buckling of thin and shallow annular spherical shells of reinforced functionalities with ring reinforcers on the elastic foundations under external uniform pressure and thermal and thermo-mechanical loading. The boundary condition of the shell is simply supported; also, the elastic environment is assumed to be baxsed on two parameters of the proposed Winkler and Pasternak model for the elastic substrate and the properties of the material are temperature dependent. The distribution of shell material follows the power law of functionaly graded materials. The reinforcements are made of ceramic and are circular. The present analysis is baxsed on the Lekhnitskii method. The boundary strain relations are obtained with respect to the non-linear relations of Von Karman-Donnell and the classical theory of shells. For nonlinear static solution of the problem, the tension function and Galerkin method are used. The effect of geometric parameters, elastic foundation stiffness, volumetric fraction index, and also the effect of the dependence of material properties on temperature on the post-buckling of functional graded spherical shells for the above mentioned loads have been investigated.