The relevance of the interstitial model for the metallic bond has been studied on 2D simple metal. lattices : the lithium square lattice and the magnesium triangular one. As on 1D systems the valence electron density is essentially interstitial on both systems. However, the magnetic treatment of the inverse lattice problem-up to now always associated with the interstitial description of simple metals-was proven false on the magnesium lattice which remains highly delocalized, The reasons of the different behavior of the Li and Mg systems have been investigated, as well as the conductivity problem associated with a magnetic description of the inverse lattice. A phase transition, semiconductor versus insulator, has been exhibited on the Mg lattice. The insulator phase (long distances) corresponding to an atom-centered solution, the semiconductor phase (short distances) corresponding to an interstitial solution.