The fundamental period of the seismically isolated buildings may be close to that of the long period pulses of near-filed earthquakes, leading to very large lateral displacements in isolators, which in turn can considerably reduce the stability of isolators, increase the chance of collision of the isolated buildings to adjacent buildings, or even result in overturning of the isolated buildings. Therefore, it is important to control these types of buildings and reduce the amount of lateral displacement in their isolating system. In this study, by conducting a series of time history analyses for a set of five multi-story steel buildings with various numbers of stories from 3 to 14, each having a very stiff core structure and a set of crosswise viscous dampers, connecting the building structure to the core structure at the lowest and the top floors, as well as the same structures without the core structure and dampers, the effect of stiff core and dampers in reducing the lateral displacement at isolators has been shown. Results indicate that by the proposed technique, the lateral displacement of the base isolation system is significantly decreased particularly for low-rise buildings.