Rotary ultrasonic machining is a costeffective machining method for hard and brittle materials. The ultrasonic vibration system is an important component for the rotary ultrasonic machining．Numerical simulation of ultrasonic transducer and horn in ultrasonic vibration system was done with finite element analysis software ANSYS. Its important parameters, such as the resonant frequency and amplification factor, were obtained. The influences of different transition circular radius and horn profiles on the performance of ultrasonic longitudinal vibration were analyzed.