The purpose of this study is to obtain the damping characteristics for reinforced concrete high rise stacks. Microtremors of those stacks were all the time. Free vibration waves were theoretically made using random decrement technique. Therefore, the damping ratios were evaluated from those free vibration waves. Parameters for the damping evaluation were employing by logarithmic decrement method or regressional analysis method analytically. The estimated damping ratios were belower than 1.0%.