This article deals with vibration analysis of clamped (C-C) and freely supported (Fs-Fs), truncated and complete conical shells on elastic foundations with continuously graded volume fraction. The functionally graded material (FGM) properties are assumed to vary continuously through the thickness of the conical shell. First, the basic relations, i.e., the dynamic stability and compatibility equations, of FGM truncated conical shells on the Pasternak-type elastic foundation are obtained. The displacement and Airy stress function are sought depending on a new parameter lambda. The parameter lambda depends on the geometry of the shell and the loading and boundary conditions. By applying the Galerkin method to the foregoing equations, the dimensionless frequency parameters of FGM conical shells on the Pasternak-type elastic foundation for two boundary conditions are obtained. Furthermore, the parameter lambda which is included in the formulae is obtained from the minimization of the dimensionless frequency parameters. Finally, the effects of the stiffness of the foundation, boundary conditions, variations of the conical shell characteristics, and composition profiles on the values of the dimensionless frequency parameters are studied. The results are validated through comparison of obtained values with those in the literature.