The aim of this study is to investigate the variation in response quantities of buildings seismically isolated by lead rubber bearings (LRBs), depending on how the superstructure is modeled in the analyses. For this purpose, two distinct seismically isolated structures with 4- and 9-stories are idealized by (i) a single-degree-of-freedom model (SDOF), (ii) a two-degree-of-freedom model (2DOF), (iii) a 3D model and subjected to near-fault earthquake excitations through nonlinear response history analyses (NRHA). In all of the structural models, the hysteretic behavior of LRBs is represented by a deteriorating force-displacement curve in which the strength of bearing decreases gradually during cyclic motion due to the lead core heating. Analyses are performed by OpenSees and the response quantities considered are floor drifts and floor accelerations for superstructures and maximum isolator displacements for isolation systems. In order to assess the influence of the superstructure modeling approach on selected response quantities, results of analyses with SDOF, 2DOF, and 3D models are compared with each other. Furthermore, in order to highlight the significance of hysteretic representation used to model LRBs, a non-deteriorating force-displacement curve, where lead core heating phenomenon is ignored, is also considered to idealize LRBs in the case of a 3D superstructural model. Results showed that the SDOF model overestimates the isolator displacements obtained from the 3D model and the 2DOF model is effective only in estimating mid-story response quantities of the 3D model.