This paper presents results of calculations performed according to our own semi-empirical mathematical model of critical vortex excitation. All calculations are carried out using own computer program, which allows the simulation of both the across-wind action caused by vortices and the lateral response of analysed structures. Vortex excitation simulations were performed in real time taking into account wind-structure interaction. Several structures of circular cross-sections were modelled using a FEM program and calculated under the action of critical vortex excitation. Six steel chimneys, six concrete chimneys and two concrete towers were considered. The method of selection and estimation of the experimental parameters describing the model are also presented. Finally, the results concerning maximum lateral top displacements of the structures are compared with available full-scale data for steel and concrete chimneys.