Energy dissipation as a means of reducing the seismic response of structures has become a popular topic among researchers and structural engineers who have developed and implemented devices, such as friction dampers, fluid dampers, and isolators, in the design or retrofit of structures. However, a natural source of energy dissipation is the interaction between a structure, its foundation, and the supporting soil medium. To account for this frequency-dependent energy dissipation in dynamic analysis based on modal superposition, relatively simple and practical systems-identification methods are presented to estimate the composite modal damping ratios for the significant modes of vibration. SSI experiments and analysis of simple theoretical models using this method have yielded relatively large modal damping ratios in certain situations for structures such as short to mid-rise buildings, short-span bridges, flat bottom fuel storage tanks, offshore concrete gravity platforms, nuclear power plant containments, and nuclear waste processing plants.