In this paper, the non-linear buckling of the truncated conical shell made of functionally graded materials (FGMs) surrounded by an elastic medium has been studied using the large deformation theory with von Karman Donnell-type of kinematic non-linearity. A two-parameter foundation model (Pasternak-type) is used to describe the shell foundation interaction. The FGM properties are assumed to vary continuously through the thickness direction. The fundamental relations, the modified Donnell type non-linear stability and compatibility equations of the FGM truncated conical shell resting on the Pasternak-type elastic foundation are derived. By using the Superposition and Galerkin methods, the non-linear stability equations for the FGM truncated conical shell is solved. Finally, influences of variations of Winkler foundation stiffness and shear subgrade modulus of the foundation, compositional profiles and shell characteristics on the dimensionless critical non-linear axial load are investigated. The present results are compared with the available data for a special case. (C) 2013 Elsevier Ltd. All rights reserved.