High Damping Rubber Bearings (HDRBs) are among various types of laterally flexible isolation system elements that effectively protect structures from detrimental effects of earthquakes by lengthening their fundamental periods. However, large isolator displacements resulting in strains larger than 100% may come into scene in case of near-fault ground motions containing long-period and large-amplitude velocity and/or displacement pulses. This is particularly important when HDRBs are used since the post-yield stiffness of an HDRB increases due to inherent strain hardening characteristics when a threshold isolator displacement limit is exceeded. Therefore, it may be critical to consider the stiffening of HDRBs in modeling of these elements for accurate seismic response evaluation of the buildings equipped with HDRBs that are located in near-fault regions. In this study, the significance of stiffening of HDRBs on the response of base-isolated buildings is investigated by conducting nonlinear time history analyses of benchmark six-story base-isolated buildings which employ HDRBs that are represented by non-stiffening or stiffening models under both historical and synthetic near-fault ground motions of various magnitudes and fault distances. The structural response parameters included in the comparisons are base displacements, story drifts, and floor accelerations. It is found that, the significance of stiffening of HDRBs on the response of base-isolated buildings under near fault earthquakes becomes more prominent as the earthquake magnitude increases and the fault distance decreases and thus suggestions for modifications to seismic code regulations are made accordingly. (C) 2016 Elsevier Ltd. All rights reserved.