In this study, the vibration and stability of freely supported FGM truncated and complete conical shells subjected to uniform lateral and hydrostatic pressures are investigated. The functionally graded material properties are assumed to vary continuously through the thickness of the conical shell. The variation of properties followed an arbitrary distribution in terms of the volume fractions of the constituents. At first, the basic relations, the dynamic stability and compatibility equations of FGM truncated conical shells are obtained. By applying the Galerkin method, to the foregoing equations, the buckling pressures, fundamental cyclic frequencies and corresponding wave numbers of FGM conical shells are obtained. Furthermore, parameter lambda which is included in the obtained formulas is get from the minimum conditions of critical stresses and frequencies. Finally, carrying out some computations, the effects of the variations of conical shell characteristics and material composition profiles on the values of buckling pressures and fundamental cyclic frequencies have been studied. The results are validated through comparison of obtained values with those in the literature. (C) 2008 Elsevier Ltd. All rights reserved.