In this paper, the overall damping as function of the velocity of vibration of two tall structures subjected to wind is studied. The overall damping ratio is studied by means of two simple, but representative and complementary models and it is compared with that identified in two buildings in The Netherlands. In the models, the soil-structure interaction is computed using the cone model for embedded foundations developed by Wolf. Relevant parameters of the structure are identified by means of experimental data and Jeary's damping predictor. The results of the modelling show a large contribution of the foundation damping ratio to the overall damping ratio when soft soil conditions are considered.