From the analysis of experiments relative to the formation of a passive layer at the Li-solvent interface a model is proposed in order to describe the gross features concerning the growth of this layer. In this model the growth is initiated by chemical reactions partially counterbalanced by a poisoning process. The model which works at a mesoscopic scale is simulated on a two-dimensional lattice. A quantitative analysis of the results shows that this model appears as the superposition of the Eden model which describes the structure of the front and a similar percolation process which determines the properties of the bulk part of the layer as its porosity. A second model in which the corrosion is taken into account is introduced. It is analyzed in a very simple case in which there is no poisoning. The corrosion induces a restructuring in the layer and this gives rise to a porosity in the bulk part of the layer. Some unexpected results are interpreted.