A computational model developed based on the phase-field approach is used to model domain structures in ferroelectric thin films and to quantify the effects of strain and applied electric field on the microstructural evolution, and on the induced dielectric, electrostrictive, and piezoelectric film properties. Theoretically predicted vortex-like polydomain and experimentally observed bidomain and monodomain film morphologies are modeled using the continuum phase-field approach. A nonlinear finite element method is used to solve the boundary value problems relevant to ferroelectric thin films. The computed results agree with the Kittel law for specific ranges of film strain. Simulations that track the domain structure evolution and compute ferroelectric thin film properties given the film dimensions and the imposed electromechanical boundary conditions are also reported.