A method of using ultrasonic waves to measure contact states between a workpiece and dies during stamping has been developed. The method is based on the fact that ultrasonic waves are reflected at the boundary of air gaps between a workpiece and a die. In our previous studies, the experimental and numerical analysis results for flat and V-shaped stamping dies show that the contact state can be monitored using ultrasonic waves. However, machine parts made by stamping consist of not only flat surfaces but also inclined or curved surfaces. When an ultrasonic wave is incident on an inclined or curved surface, modal conversion of the ultrasonic wave occurs. Thus, acoustic fields near the boundary surface become complicated. In this study, we investigate the reflection and transmission characteristics of ultrasonic waves at the contact surface between cylindrical stamping dies. The following results were obtained: (1) the reflection of ultrasonic waves was affected by the die shape but (2) when a thin metal plate was firmly attached to the stamping die, the transmitted waves were not greatly affected by the die shape.