This talk concerns the Proudman resonance. It is a resonant response in shallow waters of a water body on a traveling atmospheric disturbance when the speed of the disturbance is close to the typical water wave velocity. In order to explain this phenomenon, I prove a local well-posedness of the water waves equations with a non constant pressure at the surface, taking into account the dependence of small physical parameters. I also justify rigorously the historical work of Proudman. Finally, I consider the linear water waves equations and give dispersion estimates in order to extend the Proudman resonance to deeper waters. To complement these asymptotic models, I present some numerical simulations.