A typical single-element High Intensity Focused Ultrasound (HIFU) transducer has a spherical shell in order to focus the acoustic energy onto the focal spot. In a prototype PZT transducer we constructed, a mode of plate wave propagation in the shell was experimentally observed in addition to the uniform thickness vibration mode. Such an unwanted wave component may deform the ultrasonic power deposition pattern, which can potentially influence the therapeutic effects. In this study, we analyzed the vibrating behavior of a spherical piezoelectric transducer in two ways: by the reconstruction of the sound source distribution from a measured pressure field and by a numerical simulation of vibration based on a Finite Element Method (FEM). In the two-dimensional Fourier analysis performed in both time and space domain, the radial wavenumber spectrum showed a high peak, second to the highest peak corresponding to the uniform vibration. This corresponds to the waves propagating from the circumference towards the center of the spherical transducer like a symmetric mode of leaky Lamb waves. The leaked waves propagate at a constant angle with the shell surface in water and form a relatively large lobe on the axis at the nearside of the geometric focus. This nearside lobe, also observed in the measurement, may cause additional near field heating of tissues.