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Abstract: In this paper, suppression of the dynamic response of tall buildings, supported on elastomeric bearings with both linear and nonlinear behaviors, is studied. The isolated building is modeled as a shear-type structure having one lateral degree of freedom at each story level. The elastic supports are modeled as an additional degree of freedom having three unknown parameters: mass, stiffness, and damping ratio. The main objective of the paper is to find the optimal values of the parameters of the base isolation system, using genetic algorithms (GAs), to simultaneously minimize the displacement of the building''s top story and that of the base isolation system. In order to simultaneously minimize the objective functions, a fast and elitist non-dominated sorting genetic algorithm (NSGA-II) approach is used to find a set of Pareto-optimal solutions. The optimal values of the parameters of the base isolators, namely: their mass, stiffness, and damping ratio are evaluated using the GAs by taking into account the nonlinearity of the isolator bearings to minimize the objective functions. Moreover, in order to solve the undesirable horizontal displacement of the lead-rubber bearings, a new method called the “independent story” (IS) system is proposed in this investigation. This system works as a big tuned mass damper (TMD) system, without using any additional damping or stiffness devices except those of the structure itself. Either one full story of the building or even a part of one story can be considered the IS system. For a numerical example, a ten-story building located in Mashhad, Iran is chosen. From the numerical study, the NSGA-II approach was found to be strongly effective in evaluating the optimal values of the parameters of the isolator bearings and minimizing the structural responses. [Copyright &y& Elsevier]