A theoretical model and mathematical description for silicon micromachined electrostatic or capacitive ultrasonic imaging transducers have been developed. According to the model the basic performance parameters of such a transducer, such as natural frequencies, eigenfunctions, resonance and anti-resonance frequencies, and the mechanical impedance of the diaphragm can be predicted from the geometry of the transducer and property parameters of materials used. The paper reveals that this type of transducers has two basic operation modes, corresponding to the resonance of a mass-spring oscillator comprised of the diaphragm and the air cushion, and the first-order bending mode of the diaphragm itself respectively, and presents an optimal method for extending the bandwidth by making the two modes coupled, and thereby provides a theoretical basis for the optimal design.