The A wave propagation was first studied on 200-mm-long plane plates made of brass. The plates were 0.2 or 0.1 mm thick. The external fluid was always distilled water, and air, water, propanol, or glycol was used as internal fluids. With propanol or glycol, a second wave was observed, called A[sup *], similar to the A wave but having a strong attenuation in the direction of propagation. Using time frequency techniques, group dispersion curves were shown to be a function of the frequency thickness product in the range 0.1--1 MHz mm. When possible, the phase velocity was derived from experimental results using the phase of the signal spectrum. Experimental results presented a very good agreement with theoretical values. The A and A[sup *] wave propagations were then investigated using cylindrical brass boxes. The thickness was also 0.2 or 0.1 mm and the radius was 60 mm. The box was filled with air, distilled water, propanol, or glycol. The experimental dispersion curves were comparable to those in the case of plane plates. If propanol or glycol were used, A[sup *] or A waves (respectively) were detected tangentially. Their attenuation was also measured.