In this study, the non-linear dynamic analysis of functionally graded (FG) truncated conical shells surrounded by an elastic medium has been investigated using the large deformation theory with von Karman-Donnell-type of kinematic non-linearity. The material properties of FG truncated conical shell are assumed to vary continuously through the thickness direction. The Pasternak model is used to describe the reaction of the elastic foundation on the FG conical shell. The fundamental relations, the non-linear motion and compatibility equations of FG truncated conical shells surrounded by an elastic medium are derived. By using the Superposition method, Galerkin method and Harmonic balance method, the problem of non-linear vibration of the FG truncated conical shell surrounded by an elastic medium is solved. Finally, the influences of variations of the elastic medium, compositional profiles and conical shell characteristics on the frequency-amplitude relations are investigated. The present results are compared with the available data for a special case. (c) 2012 Elsevier Ltd. All rights reserved.