The distribution of the maximum response of structures to wind actions is usually determined by Davenport’s model assuming that the structural response is a random stationary Gaussian process and the up-crossings of high response thresholds are rare independent events. The hypothesis that wind actions are stationary limits analyses to synoptic phenomena. The hypothesis that wind actions are Gaussian implies that turbulence is small and atmospheric stratification is neutral. The hypothesis that the up-crossings of high response thresholds are rare independent events raises some doubts with regard to structures with low fundamental frequency and/or small damping coefficient. This paper aims at inspecting this topic with special regard to the properties of real wind velocity records and their influence on the distribution of the maximum response, the classical use of theoretical models and their reliability for flexible and low damped structures. Analyses are carried out in the classical framework of stationary Gaussian processes.