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Unbonded fiber-reinforced elastomeric isolators (UFREIs) are a potentially low-cost and viable alternative for application as base isolators in low-rise buildings due to their adaptive characteristics. The behavior is denoted adaptive because the device exhibits well-defined lateral softening and subsequent substantial stiffening responses depending on the loading level. Since adaptive characteristics could have a significant effect on the seismic response of base-isolated structures, proper modeling of adaptive devices is crucial. There are several numerical modeling techniques for considering the adaptive characteristics of UFREIs. However, to date, none accurately fit the experimental hysteresis loops of UFREIs at large displacements where there is more dissipated energy due to full rollover. In this paper, an impact model is added to the leading numerical models of UFREIs (i.e., the Bouc–Wen model with a fifth-order polynomial and the algebraic model) to accurately capture the force-displacement hysteresis in lower and larger displacement amplitudes. The proposed impact model is then validated using prior experimental cyclic loading tests for square and rectangular specimens and shake table tests for different earthquake records. The effect of the impact model was also investigated through comparison with the response of the existing phenomenological models (e.g., the Bouc–Wen model with a fifth-order polynomial, the algebraic model, and the elastomeric bearing (Bouc–Wen) element). The results show that incorporating the impact model will improve the ability of the current numerical models to capture the behavior of UFREIs, particularly at larger amplitudes. [ABSTRACT FROM AUTHOR]