Rolling isolation systems (RISs) protect mission-critical equipment and valuable property from earthquake hazards by decoupling the dynamic responses of vibration-sensitive objects from horizontal floor motions. These responses involve the constrained rolling of steel balls between bowl-shaped surfaces. The light damping of steel balls rolling between steel plates can be augmented by adhering thin rubber sheets to the plates, thereby increasing the rolling resistance and decreasing the displacement demand on the RIS. An assessment of the ability of lightly- and heavily-damped RISs to mitigate the hazard of seismically induced failures requires high-fidelity models that can adequately capture the systems' intrinsic nonlinear behavior. The simplified model presented in this paper is applicable to RISs with any potential energy function, is amenable to both lightly- and heavily-damped RISs, and is validated through the successful prediction of peak responses for a wide range of disturbance frequencies and intensities. The validated model can therefore be used to compute the spectra of peak floor motions for which displacement demands equal capacity. These spectra are compared with representative floor motion spectra provided by the American Society of Civil Engineers 7–10. The damping provided by rolling between thin viscoelastic sheets increases the allowable floor motion intensity by a factor of 2–3, depending on the period of motion. Acceleration responses of isolation systems with damping supplied in this fashion do not grow with increased damping, even for short-period excitations. Copyright © 2013 John Wiley & Sons, Ltd.