Abstract: Lasers and water jets are traditional methods for auxiliary punching of fragile materials such as ceramics, however, the equipment used is large and complex. When processing fragile materials such as ceramics, the equipment using ultrasonic vibration with a hole amplitude converter is simpler and smaller than the traditional equipment using laser and water jet. Ultrasonic machining has been paid more attention recently. In this paper, a uniform ultrasonic horn with an inner cylindrical hole or an inner cone hole is proposed to do the punching work. Based on the analytical method, the frequency equations and performance parameters expressions of the two types of horns are derived, and the influences of different geometrical sizes on performance parameters are analyzed. The finite element method is used to calculate the distributions of stress and vibration displacement along the axial direction of the two horns at their resonant frequencies. The results show that the amplification factor of the apertured horn is greater than that of the solid uniform rods under the same area coefficient and the same resonant frequency; and the amplification factor of the horn with tapered hole is smaller than that of the horn with cylindrical hole, but the stress distribution of the former is smoother and its maximum value is less.