ESDU 96030 describes the nature of the lateral response to vortex shedding of structures of circular or of polygonal cross section with more than eight sides. A method is developed for calculation of this response together with the data required to implement it. It takes account of the response to buffeting by across-wind atmospheric turbulence components, using the methods of ESDU 89049. Comparisons of predictions with both model and full-scale measurements, and a discussion of methods of reducing response to vortex shedding are included. ESDU 96031 introduces a program running in Excel that implements the method. The method treats the following conditions: structures that are parallel-sided, tapered and stepped with smooth or rough surfaces (if ancillary structures are attached such as ladders they must be entirely in the main structure wake for the method to apply), cantilevered or between end fixings, vertical, horizontal or inclined in flow that is uniform or shear, smooth or turbulent, with natural atmospheric turbulence or simulated turbulence as in a wind-tunnel.