The effect of uniaxial external stress fields applied during the cooling do
wn from the deposition temperature on the domain structure of epitaxial fer
roelectric or ferroelastic films is investigated using the domain stability
map. This map predicts stable domain structures and is constructed in the
coordinates of the misfit strain between the cubic substrate and the film,
and the tetragonality of the film. It is shown that with the application of
a stress field perpendicular to the film-substrate interface, perfectly c-
axis oriented films may be obtained.