  Combining effective Hamiltonian and direct $ab$ $initio$ computation, we
obtain the phase diagram of SnTiO$_{3}$ with respect to epitaxial strain and
temperature, demonstrating the complex features of the phase diagram and
providing insight into the epitaxially strained SnTiO$_{3}$, a presumably
simple perovskite. In the phase diagram, two triple points are found, which may
be exploited to to achieve high-performance piezoelectric effects. On the other
hand, despite the inclusion of the degree of freedoms related to oxygen
octahedron tilting, it is found that ferroelectric displacements dominate the
structural phases over the whole strain misfit range. Finally, it is shown that
the SnTiO$_{3}$ can be converted from hard to soft ferroelectrics with
epitaxial strain.
