Damping has a significant effect on the dynamic behavior of base-isolated structures. It reduces the overall response and prevents resonance phenomena. Sources of damping are the dissipation of energy in the elastomeric bearings and in the soil as radiation damping. These effects are evaluated using two approaches: the complex eigenvalue approach which is mathematically correct but uses the damped vibration modes and an energy method which is simple but less accurate. The two methods are compared and the accuracy of the energy method is assessed. Examples of frequencies and modal damping of base-isolated structures are given.