Motion within a soft muddy bottom under small amplitude wave action is briefly examined using an analytical approach to gain insight into the mechanism by which coastal mud responds to water waves. The bed is modelled as a viscoelastic body using the Voigt model. The model's results on interface shear stress and wave damping show acceptable agreement when compared to laboratory data. This model is an extension of the one developed by MacPherson [3], since it considers the continuity of the shear stress through the watermud interface, taking into account a thin water boundary layer upon the interface. It can be concluded that: