Using the Hartree‐Fock approximation we analyze the properties and stability of the filled (one doped hole per stripe site) vertical stripes (VS) and diagonal stripes (DS), found in the two‐dimensional Hubbard model at two representative doping levelsx= 1/8 andx= 1/6, by varying the ratio of the on‐site Coulomb repulsionUto the hopping elementt. In the weak coupling regime ofU∼ 3.5tthe stability of VS is best explained by the solitonic mechanism which leads to the kinetic energy gain due to the hopping perpendicular to the stripes, while DS have a lower potential energy which explains their stability in the regime of largeU. The results obtained beyond the Hubbard model are shortly reviewed as well. © 2003 American Institute of Physics