This paper presents a survey of a lot of full scale damping measurements of steel chimneys. Based on these measured values damping values are proposed to be used for the fatigue assessment of steel chimneys due to vortex excited vibrations. The proposed values partially differ from the values which are given by several codes for the design of steel chimneys. Furthermore for the specified types of construction of steel chimneys the lowest value is given which has been measured and which is known by the authors. Thus, for chimneys for which a high reliability class is intended, a damping value is given which allows the calculation of the biggest vortex excited amplitude to be expected according to the latest findings.