<p>The current paper is the first research on the nonlinear hygro-thermo-mechanical postbuckling behaviors of spiderweb-stiffened sandwich spherical shells (SShs) and circular plates (CPls). The shells/plates are made of functionally graded graphene platelet-reinforced composite (FG-GPLRC) with a porous core and stiffened by FG-GPLRC parallel and/or meridian stiffeners. The investigated structures are subjected to combined effects of the external pressure, temperature, and moisture changes. The Donnell shell theory (DST) is employed to describe the displacement field taking into account von Kármán geometric nonlinearities. Lekhnitskii’s smeared stiffener technique is expanded to determine the stiffness components of the stiffened shells/plates. By choosing the polynomial solution form for the displacements and using the Ritz energy method, the governing equations of the problem are established, and the nonlinear hygro-thermo-mechanical postbuckling curves of the structures are obtained. The remarkable influences of various parameters such as material parameters, geometrical parameters, porous core, temperature, and moisture on the nonlinear postbuckling responses of the stiffened sandwich SShs/CPls are illustrated in the numerical example.</p>