The strain, inevitably existing in ferroelectric films and devices, is an important factor for determining their polarization properties and performances. It requires an understanding of the effects of strain on polarization dynamics of ferroelectric film. Considering the strain effect, an analytic thermally activated electric polarization-switching model was developed for the study of the polarization properties of ferroelectric films. Using this model, we successfully simulated the time dependent polarization reversal, the coercive field, the polarization switching time, and the polarization hysteresis loops as a function of the lattice mismatch, external applied stress, applied electric field, and temperature. Theoretical predications of the model are in good agreement to experimental observations and they reinforce the possibility of using sophisticated thin film fabrication techniques such as lattice mismatch strain to engineer ferroelectric thin films structures and devices with controlled properties. Our study offers clear analytical relations that can be easily used in future studies of ferroelectrics.