  We present a simple analytical model for the determination of the stable
phases of strained heteroepitaxial systems in (1+1) dimensions. In order for
this model to be consistent with a subsequent dynamic treatment, all
expressions are adjusted to an atomistic Lennard-Jones system. Good agreement
is obtained when the total energy is assumed to consist of two contributions:
the surface energy and the elastic energy. As a result, we determine the stable
phases as a function of the main ``control parameters'' (binding energies,
coverage and lattice mismatch). We find that there exists no set of parameters
leading to an array of islands as a stable configuration. We however show that
a slight modification of the model can lead to the formation of stable arrays
of islands.
