The cavity model is a wide-spread powerful empirical approach for the numerical simulation of microstrip antennas. It is based on several hypotheses assumed a priori: a dimension reduction in the cavity, that is, the zone limited by a metallic patch and the ground plane in which is fed the antenna, supplied by the additional condition that the open sides of the cavity act as magnetic walls. An additional important assumption of this model consists in an adequate description of the singular field behavior in the proximity of the edge of the patch. A simplified two-dimensional problem incorporating the main features of the field behavior near the edge of the patch and inside the cavity is addressed. The method of matched asymptotic expansions is used to carry out a two-scale asymptotic analysis of the field relatively to the thickness of the cavity. All the empirical hypotheses at the basis of the derivation of the cavity model can thus be recovered. Proved error estimates are given in a simplified framework where the dielectric constants of the substrate are assumed to be 1 in order to avoid some unimportant technical difficulties.