Two methods of calculating the damping ratio for structures on compliant foundations are presented. One method employs the calculation of the system damping ratio from the dynamic amplification factor, the other the modal damping ratio from energy considerations. The numerical results for both methods are compared and interpreted. Three sources of damping are considered: inter-storey damping, radiation damping, and foundation material damping. The numerical results demonstrate that with the introduction of compliant foundations the damping ratio of the system can be larger or smaller than that of the corresponding fixed-base structure. Material damping in the foundation soil has been shown to contribute significantly to the over-all damping ratio.