At present, the analysis of boundary value problems for the Helmholtz equation is widely used to study the propagation of sound in marine acoustic waveguides. The ocean bottom can be considered as interface between different media. A characteristic feature of the considered plane-layered waveguide model is the presence of inhomogeneities in the physical properties of the water layer, which are described in the first approximation by the inhomogeneous speed of sound. Presented model is also taking into account the elastic properties of the bottom. The paper presents a new analytical solution to the problem of sound propagation by a point source for this model of waveguide.