We derive analytical expressions for the non-zero stress and strain tenser elements of cubic epitaxial films on (1 1 3) surfaces. We have evaluated these expressions for systems with the greatest immediate future technological promise, emphasizing Ge on Si(1 1 3). In this case there are compressive stresses along [3 3 (2) over bar] and [(1) over bar 1 0] of 6.39 and 5.77 GPa, respectively. Comparing with previous experimental work, we conclude that the Ge nanowire growth morphology on Si(1 1 3) elongated along [3 3 (2) over bar] is not caused by film stress and strain effects. Taking other theoretical work into consideration leads to the conclusion that in this case the nanostructure elongation direction arises from the anisotropic surface stress properties of the surface monolayer, including the heteroepitaxial components.