This paper discusses a vibration control performance of damping devices installed in a building structure. The motivation of this study comes from the recognition that we often observe much smaller damping performance than is expected from the pre-analytical study in many application projects. Emphasis is placed on the stiffness increase of the structure that is equipped with those damping devices. The relationship between the damping and stiffness augmentation is analytically obtained and expressed in a closed form solution. Therefore, the performance in terms of damping factor is easily evaluated by means of real eigen-value analysis. Numerical simulation is also conducted to ascertain the validity of the proposed method for a relatively large structure under earthquake disturbances.