During very strong earthquakes, seismically isolated buildings may experience large horizontal relative displacements, which may lead to poundings if an insufficiently wide clearance is provided around the building. This paper investigates, through numerical simulations, the effectiveness of using rubber bumpers, which could be attached at locations where it is likely to have impacts, in order to act as shock-absorbers. For the simulation of the dynamic behavior of such rubber bumpers during impacts, a nonlinear force-based impact model, which takes into account the finite thickness of the rubber bumpers, has been developed. Subsequently, a series of parametric analyses are performed to assess the effect of the gap size, the earthquake characteristics and the thickness, compressive capacity and damping of the bumpers. The stiffness of the moat wall is also parametrically considered during poundings of a seismically isolated building, as another potential mitigation measure for poundings of seismically isolated buildings.