Strain and applied external electric fields are known to influence domain evolution and associated ferroelectric responses in ferroelectric thin films. Here, phase-field simulations are used to predict equilibrium domain structures and polarization-field (P-E) hysteresis loops of lead zirconate titanate (PZT) thin films under a series of mismatch strains, ranging from strongly tensile to strongly compressive. In particular, the evolution of domains and the P-E curves under different applied strains reveal the mesoscale mechanism, the appearance of in-plane polarization during domain switching, that is responsible for a relatively small coercive field and remnant polarization. A Landau energy distribution is analyzed to better understand the domain evolution under various strain conditions. The results provide guidance for choice of mismatched strains to yield the desired P-E hysteresis loops and the domain structures.