Abstract This paper presents an analytical approach to investigate the effects of tangential edge constraints on the buckling and postbuckling behavior of functionally graded flat and cylindrical panels subjected to thermal, mechanical and thermomechanical loads and resting on elastic foundations. Material properties are assumed to be temperature independent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Governing equations are derived basing on the classical shell theory incorporating von Karman–Donnell type nonlinearity, initial geometrical imperfection and Pasternak type elastic foundations. Approximate solutions are assumed and Galerkin procedure are applied to obtain explicit expressions of buckling loads and load–deflection relations. The effects of in-plane edge restraint, elastic foundation, temperature and imperfection on the nonlinear response of the panels are graphically analyzed.