ESDU 83009 provides damping data for the estimation of the small amplitude response of tall buildings to wind excitation. Data enable the modal damping, expressed as a fraction of critical damping, to be estimated for the first translational modes of vibration parallel to the two principal axes of deformation. The method applies to buildings of regular construction over 20 m (65 ft) tall. The modal damping ratio is given by the sum of the modal structural and aerodynamic damping ratios. The modal structural damping ratio may be estimated from simple design charts based on full-scale measurements, and the modal aerodynamic damping ratio is given by simple formulae. The effect of foundation damping is discussed. The mechanisms of damping in a tall building are explained, and the effect of increasing amplitude of vibration on the modal damping is discussed. Full-scale test results illustrate the effect. Methods of measuring the modal damping, with an explanation of the accuracy of measured values, are outlined. Various techniques for increasing the modal damping are considered. The mode-generalised parameters required for the response calculations by the normal-mode method are presented, and their application in the design of damped scale models of full-scale buildings is discussed. Other modal damping expressions commonly used in the study of tall building response are given.