Abstract This paper deals with the non-linear response of sandwich curved panels exposed to thermomechanical loadings. The mechanical loads consist of compressive/tensile edge loads, and a lateral pressure while the temperature field is assumed to exhibit a linear variation through the thickness of the panel. Towards obtaining the equations governing the postbuckling response, the Extended Galerkin’s Method is used. The numerical illustrations concern doubly curved, circular cylindrical and as a special case, flat panels, all the edges being simply supported. Moveable and immoveable tangential boundary conditions in the directions normal to the edges are considered and their implications upon the thermomechanical load-carrying capacity are emphasized. Effects of the radii of curvature and of initial geometric imperfections on the load-carrying capacity of sandwich panels are also considered and their influence upon the intensity of the snap-through buckling are discussed. It is shown that in special cases involving the thermomechanical loading and initial geometric imperfection, the snap-through phenomenon can occur also in the case of flat sandwich panels.