The Guyana coastal system is characterized by very thick deposits of Amazon mud and high mud concentrations in its coastal waters. The mud deposits can be quite soft and may liquefy under incoming waves. Subsequently, the liquefied mud damps the incoming waves effectively. This paper presents a simple model to predict wave attenuation over soft (fluid) mud beds. This model is based on the two-layer approach by Gade [Gade, H.G., 1958, Effects of a non-rigid, impermeable bottom on plane surface waves in shallow water, Journal of Marine Research, 16 (2) 61-82.] which is implemented in the standard version of the state-of-the-art wave-prediction model SWAN. Input to the mud wave damping module consists of the extension, thickness, density and viscosity of the liquefied (fluid) mud layer. The model is validated against small-scale wave attenuation measurements carried out in a laboratory wave flume. The model predictions agree favourably with the experimental data. Next, the model is applied to predict wave height and wave attenuation in the Guyana coastal system. Extension and thickness of the liquefiable layer could be assessed from dual-frequency echo soundings. In the absence of field data, the density of the liquefied mud layer is obtained from literature, whereas the value of the mud's viscosity had to be established by trial and error - the selected value, though, is in the range of literature values. The model predicts significant wave attenuation. The computed changes in wave energy spectrum agree qualitatively with measurements in Surinam, whereas the decrease in significant wave height agrees more or less with historic observations along the Guyana coast.