Abstract: For solving the design problems of ultrasonic vibratory system in gear machining, the gear is reduced to an annular plate firstly, the frequency equations of the transformer, which is consists of non-resonance annular plate and horn, are derived by means of the force coupling condition, boundary condition and dynamical equation secondly. Then the design parameters are got by solving the frequency equations numerically and demonstrated by experiment, their results are consistent. The theoretical method has extended the transformer design from resonance to non- resonance.