As a departure from the many continuum analyses of stability and evolution of surface shape that have been reported for crystalline materials, this paper provides a description of surface evolution based on the physics of the main feature imposed by the discrete nature of the material, namely, crystallographic surface steps. It is shown that the formation energy of surface steps depends on the sign of extensional strain of the crystal surface, and this behavior plays a crucial role in surface evolution. The nature of this dependence implies that there is no energetic barrier to nucleation of islands on the growth surface during deposition, and that island faces tend toward natural orientations which have no counterpart in unstrained materials. The continuum framework developed is then applied to study the time evolution of surface shape of an epitaxial film being deposited onto a substrate. The kinetic equation for mass transport is enforced in a weak form by means of a variational formulation. It is found that islands evolve with the features that were identified from the energy arguments. The implications of the calculations are shown to be consistent with the behavior observed during deposition of semiconductor materials in recently reported experiments. The parameters in the continuum description are obtained from atomic scale simulations.