The electromechanical properties of ferroelectric thin films under an alternating electric field and a static uniaxial compressive stress are investigated using the modified planar four-state Potts model. To implement the electromechanical properties and the coupling of the electrical and mechanical response, the mechanical energy density as well as the energy due to anisotropic switching between a-domain and c-domain are incorporated in the Hamiltonian. Besides, there are two contributions to the strain at each cell: eigenstrain and elastic strain. Our simulation results show that the longitudinal strain-electric field butterfly loop shifts downward along strain axis and that for the transverse strain shifts upward as the stress magnitude is increased. Moreover, the polarization-electric field hysteresis loop becomes a double-loop under a large compressive stress. The piezoelectric coefficient increases with the stress magnitude and reaches a maximum value at a critical stress level. It then gradually decreases to a small value at large stress magnitudes. Our results qualitatively agree with experimental ones.