The propagation of sound waves in the ocean is influenced by the acoustic characteristics of the seabed, especially in shallow water. If the seabed is considered to be an elastic or viscoelastic structure, then sound propagation will be influenced by the shear and longitudinal properties of this structure. Accordingly, this paper examines the sensitivity of sound propagation to the shear properties of the ocean floor for shallow waters and when the sound source lies in the ocean. This is motivated by predictions reported in the structural mechanics literature, which demonstrate that wave propagation in viscoelastic structures can be highly sensitive to the shear properties of the material. This investigation uses the semi analytic finite element method to undertake a set of numerical experiments. This numerical approach provides a computationally efficient way of solving the fully coupled acoustic problem, with Bergmann's equation used for the fluid, and Navier's elastodynamic wave equation for the seabed. Both elastic and viscoelastic structures are examined and predictions are reported for a range of shear properties, and the relative sensitivity of sound propagation on these shear properties is then investigated.