The lowest vibration modes of a composite beam resting on an inhomogeneous elastic foundation in the case of a clamped-free boundary condition are investigated. It is observed that the relation between the frequency and foundation constant has an effect on the valid solution of the problem. An asymptotic procedure is employed to derive the eigenfrequencies as well as the eigenforms revealing that only under certain conditions on the ratios of material parameters. Numerical illustrations are presented to confirm that the obtained asymptotic frequencies agree well with the exact frequencies in the lowest frequency range. Comparisons of asymptotic and exact displacements are also presented and a remarkable agreement is observed for high-contrast beam components.