Propagation characteristics of plate-mode waves in a wedge-shaped piezoelectric ceramic plate are described based on numerical and experimental results. Distributions of phase velocity, group velocity, and mechanical displacement are given as functions of the product of frequency F and substrate thickness D. In the experiment, the transition wherein the Rayleigh-mode wave disperses into zeroth-order antisymmetrical and symmetrical modes as it propagates on the wedged substrate is studied. The process in which the waves of these modes are reflected from the front end of the substrate and then degenerated again into the Rayleigh-mode wave is also observed and analyzed. By use of the above-mentioned characteristics, a contact ultrasonic probe is proposed which can distinguish between longitudinal and transverse vibrations. In contrast to a probe which uses a convergent beam, this probe has a resolution which is not limited by the wavelength, so it has high resolution even at low frequencies. It is confirmed experimentally that the probe can discriminate longitudinal and transverse vibrations and that it has a resolution higher than about 4 mm, which is the wavelength of a carrier wave around 1 MHz.