This paper discusses a vibration control performance of inelastic damping devices installed in a building structure under a large earthquake. It is commonly believed that the plastic deformation due to material yielding has large energy dissipation capacity as well as large damping effect on the system response just like linear viscous dampers. This paper proposes a mathematical model that depends on the feedback control theory and modern control approach to verify the damping augmentation instead of an ordinary model commonly used in the civil engineering. The author discovered that we could expect as much damping augmentation from inelastic dampers as from ordinary linear viscous dampers, but the damping effect itself is far less than we expected from a classical dynamic model. Further discussion is definitely necessary until we make a reasonable engineering decision as to which model is better to describe the real dynamics of the structure.