A study is made of the resonant oscillation modes in a three-dimensional channel filled by a heavy incompressible liquid, with a free surface at the top and an elastic membrane on the bottom. It is shown that for definite relations between the parameters of the channel and the inclusion there is a discrete spectrum, which extends only up to the waveguide cutoff frequency, in addition to the continuous spectrum of oscillation frequencies. The oscillation modes of the liquid have a localized character in the region of the inclusion.