Abstract: Based on the classical shell theory and von Karman geometric nonlinear theory, the displacement-type geometric nonlinear governing equations and simply supported boundary conditions for functionally graded shallow circular spherical shells were derived. The uniform temperature field and the external uniform pressure were considered in the derivation. The two-point boundary value problem posed by this set of governing equations and the boundary conditions was solved with the shooting method. The numerical results of axisymmetric deformation of the shells were obtained. The effects of the geometric parameters of the shell, the transverse gradient properties of the shell’s materials, the volume fraction index and elasticity modulus of the constituent materials, and uniform temperature field on the buckling equilibrium paths, upper/lower critical loads and equilibrium configurations of the shell were investigated. The numerical results show that the upper critical load of the shells decreases significantly with the increase of the volume fraction index and the decrease of the elasticity modulus of the constituent materials. The effects of the volume fraction index on the lower critical load of the shells is complicated. The rise of the uniform temperature brings obvious increase/decrease of the upper/lower critical loads of the shells. The transverse gradient properties of the shell’s materials on the effects of the buckling equilibrium paths and post buckling stable configurations of functionally graded shallow circular spherical shells with simply supported edges are very significant. Two numerical tables and some numerical curves are given for the convenience of designers.