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In this study, the non-linear stability of three-layered conical shells with functionally graded core have not been investigated previously. The purpose of this paper is to study this problem. The large deflection theory with von Karman-Donnell-type of kinematic non-linearity is used to deduce the basic equations. The basic equations are solved analytically by using superposition and Galerkin methods. The influences of several parameters on the dimensionless non-linear critical axial loads are discussed. [ABSTRACT FROM AUTHOR]