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The response reduction of reinforced concrete (RC) building structures due to soil-structural interaction has been discussed generally using simplified models idealized with an equivalent elastic sway spring, because the nonlinear characteristics and frequency dependent response of surrounding soils are not well quantified in large inelastic range. Aside from these nonlinear soil deformations, the response of RC structures on spread foundation could decrease with nonlinear base slip behavior, if the foundation base shear exceeds the friction strength at the base of the footings. The behavior has been verified through a full-scale shake table test of RC buildings with spread foundation on the concrete slab. In this paper, the upper-bound response of RC structures with a simple nonlinear sway spring is estimated generally based on dynamics theory. The potential energy of the structure is conserved during base slip, so that the maximum response of the structure during base slip is to be limited from the velocity and restoring force when the base starts to slip. The maximum velocity can be evaluated on the assumption that the maximum input acceleration acts on the structure during the preceding period of base non-slipping behavior. Therefore, the maximum restoring force can be estimated using the maximum input acceleration, the base friction coefficient, and the mass ratio of the upper structure and the foundation. The accuracy of the theoretical estimation was verified through the nonlinear responses of the models with wide range of parameters.