Base isolation systems are the most extensively applied systems as passive vibration control systems. So far extensive parametric studies have been made for the review of the performance of these systems for a decrease in torsional response in structures mostly in which the effect of soil structure interaction has been ignored. This is acceptable for the structures built only on stiff soil. In this present research, the effect of soil structure interaction has been studied on the performance of asymmetric base-isolated structures. In addition, this research aims to analyze the parameters effective on the response of these structures and present a proper distribution for the base isolation systems for a decrease in the torsional response of superstructures and base isolation systems. For this reason, several multi-storied structural models and various eccentricities have been reviewed under unilateral earthquake. The base isolation system used in this research is of an elastomeric type, which has been designed and studied for various base isolation systems. For modeling soil around a structure and considering the effect of soil structure interaction, the cone model with spring- dashpot assembly has been applied in this research. In continuation of this research, the theory of random vibrations and probability has been applied for studying a single-storied asymmetric base-isolated structure to find a better understanding of how various parameters effect on the torsional response of the asymmetric base-isolated structures. The results show that the optimum distribution of the base-isolation systems are CI=-CS/2 and CI=CS (CI and CS are defined as a center of isolators and superstructure eccentricity) for the control of the behavior of superstructures and the base isolation systems, respectively. The response of superstructures and the response of the base isolation systems will increase when the ratio of the uncoupled torsional frequency to superstructure translation frequency (?s) is increased. The review of the effect of the soil structure interaction shows that when the superstructure eccentricity is increased the effect of the soil structure will first make the response increased, but then will make it decreased. In addition, the effect of the soil structure interaction and the asymmetric status of superstructures is decreased when the ratio of the period of a base- isolated structure to that of a non-isolated structure is increased. In conclusion, the results of this research indicate that the sensitivity of the response of superstructures to the effect of soil structure interaction is much higher than that of the response of base isolation systems to the effect of soil structure interaction. Key words : Base Isolation Systems, Asymmetric Structures, Soil Structure Interaction, Cone Model, Random Vibrations.