The damping ratios of the modes as well as the natural frequencis and the mode shapes are required to characterize the modal behavior of structure. The mode shapes and the natural frequencies are determined from analytical methods or measurements accurately. But there is little analytical basis for estimating the damping ratios although they are the most important to determine the amplitude of the vibration. Especially for the cable-stayed bridges the aerodynamic damping ratios determine the amplitude of the response to wind loads. This paper is an attempt to estimate the aerodynamic damping ratios based on measured data and quasi-static theory.