The propagation of acoustic waves in a layered medium is considered for the case of an elastic plate submerged at a certain depth below the surface of a liquid‐filled half‐space. It is shown that there exist unattenuated modes for the plate‐liquid layer system which have horizontal phase velocities greater than the sound velocity in the liquid. In spite of such greater phase velocities, radiation into the liquid below does not take place because the lower surface of the plate exhibits no vertical motion. Thus, energy can be trapped in and above the plate by vibrations which leave the underlying liquid undisturbed. It is pointed out that radiation in the horizontal direction may also be very small when the above conditions of total reflection are approximately satisfied, as is indicated by the existence of low group velocities for the modes of a free plate. Attention is called to the three‐dimensional nature of such trapping, vertically by an approximate condition of no transmission across the plate, and horizontally by the simultaneous vanishing of the group velocity at nonvanishing angles of incidence. The present modes are in contrast with the usual case of total reflection and “wave guide propagation” in layered elastic media, where the horizontal phase velocity is less than the sound velocity in the liquid (lower half‐space), and the signal below the plate decays exponentially with distance from the interface. Conditions under which the present modes can arise have been found and evaluated numerically. Relations between phase velocity, wave number, and ratio of fluid layer to plate thickness are presented for a lucite plate is water. These have been compared with the results of much more elaborate calculations for the point source “singing” problem.