To characterize the supplemental damping in buildings is essential for practicing engineers to understand the resultant effect of the added damping. It is straightforward to characterize the overall system parameters representing the amount and the plan-wise distribution of the supplemental damping in single-story asymmetrical building. Nevertheless, this becomes a difficult task for multi-story two-way asymmetric-plan buildings. At first, this paper deals with this task. This research proposed a method to characterize the supplemental damping in two-way asymmetric-plan buildings. This thesis shows that we can obtain those properties from the effective one-story building (EOSB). Secondly, an approach for optimizing the placement of linear viscous dampers in two-way asymmetric-plan buildings was proposed by calculating the frequency response functions of the EOSB. This proposed approach was verified by investigating some numerical example buildings.