ESDU 90036 provides procedures for the calculation of the across-wind response of structures arising from vortex shedding. It deals with structures of non-circular cross-sectional shape and is applicable to buildings, towers, stacks and structural elements. The methods on which the calculation procedures are based have been derived from measurements on parallel-sided structures of regular cross section with sharp corners aligned symmetrically with the flow. Such shapes include those of square, rectangular, triangular and polygonal cross section and typical structural member shapes such as I- and H-beams. The effect of rounded edges and taper can be important and guidance is given on how to extend the applicability of the methods to these cases. The procedures are summarized in calculation-sheet format and provide estimates of the rms and maximum amplitude at the critical wind speed for vortex shedding and also for off-critical wind speeds. Several worked examples are included and a comparison is made between predicted and measured responses from a number of wind tunnel studies.