The new deterministic model H2U (from French “Hydrogramme unitaire universel”) is validated for two Mediterranean catchments, both in natural conditions, in the south of France and in the very anthropic catchment of Paris-Orly airport. It starts from a description of the drainage network by means of a density function of the hydraulic lengths. Through the mean water speed in the channels, this function is proved to be the unit hydrograph, or transfer function of the catchment. Moreover, in some cases, the production function can be directly known, for instance when the rain intensity is very high, or, if rain intensities are rather low, when the impervious surface area ratio is known and can be considered as the effective rainfall/total rainfall ratio. Then, the H2U model can give directly a good simulated curve of discharge, without any calibration except for the estimation of the mean water speed. The model can probably give good simulations in any situation provided that the production function has been evaluated. Even better, it can be used as the known kernel function in order to obtain the effective rainfall, i.e. the production function, by deconvolution of the actual hydrograph.