The resolution of some problems of electromagnetic scattering from random rough surfaces implies the derivation of the illumination function, especially when the geometrical optics approximation is valid. In current models, the shadowing e ects occurring for both the trans- mitter and the receiver are assumed to be independent of their azimuthal directions. This assumption makes it possible to compute separately the shadowing probabilities in each di- rection. However, if the transmitter and receiver azimuthal directions are close, these proba- bilities become strongly correlated. In such a con guration, the uncorrelation approximation induces an overestimation of the average illumination function up to 10% as well as a discon- tinuity. In this paper, assuming a surface with Gaussian process, this correlation is taken into account. Comparisons of our model with Monte Carlo simulations are made and show a very good agreement, which validates our approach.