A mathematical model of rectilinear surface waves incident on a submerged circular sill is developed. The class of waves considered consists of those for which the ratio of wavelength to water depth is large but which do not necessarily belong in the longwave category. A friction damping term is introduced into the equations of motion and the solutions obtained for the regions over the sill and in the ocean are matched by assuming a continuous surface and energy flux at the sill edge. The results show large reductions in the Q-factor of the resonance peaks brought about by friction damping. It is also found that, except at low frequency, a large number of overlapping resonance peaks which are out of phase with one another occupy a relatively narrow frequency band such that these resonance peaks effectively cancel one another. Experiments were performed to determine the friction constant used in the equations of motion and, using this friction constant, the theoretical results of wave resonance are verified.