This paper stduies the effects of initial stresses on resonance characteristics of Film Bulk Acoustic Resonator (FBAR) in thickness-extension mode. Based on the fundmental piezoelastic equations of piezoelectric material with initial stresses, the vibration equation of ideal FBAR under sines excitation voltage is derived. The solutions are then obtained by using of the boundary conditions. The series and parallel resonance frequency are listed, and the effects of initial stresses on resonance frequency, bandwidth, and effective electromechanical coupling coefficien are discussed. A numerical example is presented to show the effects. These results are very useful for the improvement of designing FBAR.