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This paper deals with the in-plane and out-of-plane vibrations of piezoelectric disc transducers, which are the main elements of ultrasonic sensors. In disc-type piezoelectric transducers, the fundamental mode is a radial mode, and the in-plane vibration of radial motion is coupled with the out-of-plane vibration of the axial motion. We developed an in-plane vibration theory, which was reported earlier, and theoretically analyzed the out-of-plane vibration and verified the theory by finite element analysis. We experimentally measured and compared the natural frequencies and verified the analysis results. In addition, we established a theoretical equation for the vibration distribution, which shows a bell-shape for the out-of-plane vibration in the thickness direction for the fundamental mode, as well as a theoretical equation of the natural frequency, which is inversely proportional to the radius.