It is shown that a waveguide in the form of a channel of infinite length filled by a two-layer heavy fluid with a free surface can have nonpropagating waves (trapped vibrational modes) along with traveling waves. These waves are localized in the region of a dynamic inclusion, i.e., a solid block (massive die) on the bottom of the channel. The appearance of such waves is due to the presence of a real discrete frequency spectrum of eigenmodes, which is located on the axis of the continuous spectrum corresponding to the divergent waves in the fluid. A relation between the geometric parameters of the channel and the characteristics of the fluid and the solid block for which such a spectrum exists is found for cases with fluids of similar density in the waveguide.