A new analytical approach for nonlinear thermal buckling of Functionally Graded Graphene Platelet Reinforced Composite (FG-GPLRC) circular plates and shallow spherical caps using the first-order shear deformation theory (FSDT) is presented in this paper. The circular plates and shallow spherical caps are assumed to be subjected to uniformly distributed thermal loads. By applying the Galerkin method, the relations between thermal load–deflection are achieved to determine the postbuckling behavior and critical buckling loads of the considered structures. Special effects on the nonlinear thermal behavior of circular plates and shallow spherical caps with five different material distribution laws, different Graphene platelet (GPL) mass fractions, and geometrical dimensions are explored and discussed in numerical examples.