In this study, the buckling analysis of functionally graded material (FGM) circular truncated conical and cylindrical shells subjected to combined axial extension loads and hydrostatic pressure and resting on a Pasternak type elastic foundation is investigated. The critical combined loads of FGM truncated conical shells with or without elastic foundations have been found analytically. The appropriate formulas for FGM cylindrical shells with and without elastic foundations are found as a special case. Several examples are presented to show the accuracy and efficiency of the formulation. (C) 2010 Elsevier Ltd. All rights reserved.