It is well known that the natural frequencies of an object are important distinguishing features which can be used in target detection and discrimination schemes. These natural frequencies are governed by the size, shape, and material composition of the object, as well as the environment in which the object resides. Since a given object of interest may reside in many different environments, it is of interest to relate the natural frequencies of an object when in free-space to the natural frequencies of the same object when immersed in a non-homogeneous environment. In this paper a perturbation formula is developed which relates the free-space natural frequencies of an object to those of the same object in the presence of a planarly layered medium. The perturbation formula is valid for intermediate spacing between the object and the nearest planar interface. Numerical results are shown for the natural frequencies of a wire in the presence of a layered medium.