Damping in the stator of a rotating machine is able to reduce the unbalance response, and increase the speed where the stability limit is reached. A convenient method to introduce damping is to support the bearings on viscoelastic elastomeric supports. This successfully adds damping but makes the analysis considerably more difficult. Viscoelastic materials have properties that depend on frequency and temperature. The determination of the run-up or run-down response of a linear machine at a constant temperature is quite straightforward based on measured material characteristics. However the introduction of transient and non-linear effects, temperature changes and model uncertainties makes the analysis difficult. This paper uses the internal variable approach to model the viscoelastic material for the transient dynamic responses, and includes an energy dissipation model. An example of a turbo molecular pump is given, and the difficulty in balancing such machines is demonstrated.