<p>This article deals with the modeling and buckling analysis for two different types of toroidal sandwich shells made of a metal-based nanocomposite foam core and titanium alloy face sheets. The sandwich shell is analyzed with two different shapes including the convex shell (positive curvature) and concave shell (negative curvature). The convex/concave sandwich shells are subjected to three different kinds of mechanical loadings including the lateral pressure, axial compressive, and hydrostatic pressure. The core of sandwich shells consists of six aluminum layers with different values of porosity reinforced by graphene nanoplatelets. Five different patterns are provided to model the porosity distribution through the thickness of the nanocomposite foam core. The nonlinear equilibrium equations of the convex/concave sandwich shell are extracted utilizing the principle of virtual displacement and considering the von Karman type of geometrical nonlinearities. The linear stability equations are also extracted for the toroidal sandwich shells by implementing the adjacent equilibrium criterion. An analytical approach based on the Airy stress function is implemented to solve the system of partial differential equations with simply supported boundary conditions. Several numerical examples are generated and presented to explore the effect of material/geometrical parameters on the shell’s critical buckling load.</p>