In this paper, the effect of a functionally graded (FG) interlayer on the non-linear stability of three-layered truncated conical shells surrounded by an elastic medium is investigated. The properties of functionally graded material (FGM) of the interlayer are assumed to be graded in the thickness direction according to a simple power law distribution. The Pasternak model is used to describe the reaction of the surrounded elastic medium on the truncated conical shell. The basic equations of the truncated conical shell with a FG interlayer resting on the Pasternak elastic foundation are derived using the Donnell shell theory with von Karman-type of kinematic non-linearity. The basic equations are solved by using Superposition and Galerkin methods. The numerical results reveal that variations of three-layered shell characteristics, Winkler foundation stiffness, shear subgrade modulus of the foundation and the compositional profiles of the FG layer have significant influences on the non-linear critical axial load. The results are verified by comparing the obtained values with those in the existing literature. (C) 2012 Elsevier Ltd. All rights reserved.