The purpose of these studies is to introduce a value D_ηаertaining to damping characteristics and ductility of metal silos from analytical response for many earthquakes. We treated the analytical models contained both the characteristics of natural period before buckling and the ratio of degradation of stiffness after buckling, by using experimental result. As a result of the studies, the following items have been made clear for D_η, 1) Influences of many kinds of earthquake, 2) Influences of natural period, 3) Influences of viscous damping, 4) Influences of degradation of stiffness.