Recent work has indicated that resonances of the water on the continental shelves may have an important effect on the flux of tidal energy in the ocean. Unfortunately, very little is known about the properties of these resonances. In order to gain some understanding, this paper considers the simple model of a rectangular continental shelf at the end of a canal. A Kelvin wave is propagated along the canal and is partly absorbed and partly reflected by the continental shelf. The canal has a depth typical of the deep ocean and the parameters of the shelf are chosen to be typical of the Patagonian shelf off Argentina. It is found that usually much of the incident energy is reflected by the edge of the shelf. But at the frequency of the dominant shelf resonance, more than 95% of the incident energy is absorbed. The structure of the main resonances and the effect on tidal observations is also considered. The dominant resonance near 14 rad day -1 has a width of about 1 rad day -1. Even if shifted in frequency into one of the tidal bands, it has such a large width that at a single locationit could not be positively identified as a resonance from tidal records. Instead a better indication of such a resonance is a geographically localized increase in the amplitude and age of the tide.