A model is developed to investigate the domain pattern and piezoelectric response across the polymorphic phase transition in strained epitaxial bismuth ferrite films. The orientations of stripelike pattern of the mixed rhombohedral and tetragonal phases are predicted as the consequence of competition between elastic and depolarization energies. The abnormally large piezoelectric response is attributed to the strain-driven softening in dielectric stiffness. The results are in good agreement with recent experimental observations and provide a guidance for developing similar strain-driven polymorphic phase transition in other related perovskite material systems.