This paper concerns the finite element method as applied to the analysis of small oscillations about the non-linear equilibrium position in elastomeric components. The capability, which was developed at Ford, has been implemented in the general-purpose finite element program, MARC. The material behavior is treated by use of a modified form of the constitutive equations derived by Lianis [Proc. Fourth International Congress on Rheology, Pt. 2, 109 (1965)] using the finite linear viscoelasticity theory of Coleman and Noll [Rev. Mod. Phys., 33 239 (1961)]. In order to establish numerical accuracy, program predictions are compared with a closed form solution for the torsional and axial vibrations in a cylinder under axial and twisting pre-loads: differences between the finite element solutions and exact results are less than two (2) percent. The measured static force deflection response and dynamic stiffness k* (= k1 + jk2) of two automotive components used for vibration attenuation and isolation purposes is shown to be in good agreement with the theoretical predictions.