The results of in situ measurements of sound speed in the marine environment in the coastal part of the Black Sea are analyzed. Based on the processing of the measurement results, a flat-layered model of waveguide sound propagation is proposed. This model includes a water layer with a non-uniform sound speed profile lying on a layer of liquid sediments (sea silt), which, in turn, lie on an elastic layer of bottom sediments. The lower boundary of the waveguide is assumed to be absolutely rigid, which approximately corresponds to a foundation in the form of rocks. For the first time, a Green's function is constructed for this model, which allows expressing the sound pressure potential as a sum of normal modes. The paper provides examples of numerical modeling.