Complex vibration sources that use diagonal slits as a longitudinal-torsional vibration converter have been applied to ultrasonic motors, ultrasonic rock drilling, and ultrasonic welding. However, there are few examples of the application of these sources to ultrasonic machining in combination with an abrasive. Accordingly, a new method has been developed for machining of holes in brittle materials by using the ultrasonic longitudinal and torsional vibration of a hollow-type stepped horn with a diagonal slit vibration converter. In this paper, we compared vibration of a uniform rod and a hollow-type stepped horn, both with diagonal slits, when the conditions of the diagonal slits are constant.