Let ${\cal S}$(g,N,p) be the Siegel modular variety of principally polarized Abelian varieties of dimension g with a Γ0(p)-level structure and a full N-level structure (where p is a prime not dividing N[ges ]3 and Γ0(p) is the inverse image of a Borel subgroup of Sp(2g,${\Bbb F}$p) in Sp(2g,${\Bbb Z}$)). This variety has a natural integral model over ${\Bbb Z}$[1/N] which is not semi-stable over the prime p if g>1. Using the theory of local models of Rapoport–Zink, we construct a semi-stable integral model of ${\cal S}$(g,N,p) over ${\Bbb Z}$[1/N] for g=2 and g=3. For g=2, our construction differs from de Jong's one though the resulting model is the same.