A new analytical approach to the nonlinear buckling and postbuckling analyses of functionally graded graphene-reinforced composite laminated cylindrical shells stiffened by functionally graded graphene-reinforced composite laminated stiffeners under external pressure taking into account the elastic foundation effect in a uniformly distributed thermal environment is presented in this paper. An improved smeared stiffener technique is developed for anisotropic stiffeners, and a special design for ring and stringer functionally graded graphene-reinforced composite laminated stiffeners is presented and successfully applied in this paper. The governing equations for the cylindrical shells are established by using the Donnell shell theory with the geometrical nonlinearity term in the von Kármán sense with the shell-foundation interaction formulated by the Pasternak elastic foundation model. A three-term solution form is chosen for the deflection, the stress function is introduced, and the Galerkin method is used to establish the nonlinear postbuckling relation. The numerical results validate the effects of the stiffeners, volume fraction of graphene, type of graphene distribution of the shell skin and stiffeners with different geometrical parameters, elastic foundation moduli, and uniformly distributed temperature changes on the nonlinear buckling and postbuckling behaviors of stiffened cylindrical shells.