The stability of Ising 180-degree domain walls with respect to appearance of chirality is analytically studied in tetragonal perovskite-type ferroelectrics taking into account electro-mechanical coupling. It is shown that the widely used approximation neglecting the elastic effects may lead to qualitatively wrong results. Sufficient condition for the stability of Ising walls is formulated only in terms of elastic and electrostrictive properties, regardless the correlation energy. We demonstrate that elasticity stabilizes Ising walls in tetragonal Pb(Zr1-cTic)O-3 and makes chiral walls unfavorable for any composition of the material (factor c), while nonelastic model predicts chirality of 180-degree walls near the morphotropic boundary.