On numerous locations in the world mud occurs in front of the coast close to river mouths. This mud can be transported to these places in fluid state or can become fluid under certain wave conditions. Fluid mud may have a strong damping effect on surface waves. Dissipation of up to 90% of the wave energy within a few kilometers has been measured. In this study, the wave model SWAN is modified to make it possible to model the dissipation of energy during the propagation of a wave field over fluid mud. A two-layer model is used to describe the water-mud-system. The upper layer represents the water and is non-hydrostatic and non-viscous. The lower layer represents the fluid mud and is quasi-hydrostatic and viscous. Based on this schematization a complex dispersion equation is derived and compared with other dispersion equations from literature. A numerical solving procedure is formulated to solve this implicit complex dispersion equation for the wave number. When the wave number is known, information on the damping is given by the imaginary part, while the real part is associated with the wave length and the propagation velocity of energy. To compute wave damping for situations in practice, the influence of mud is incorporated in the wave model SWAN. First, the energy dissipation term consistent with the dispersion equation is derived and added as a sink term to the energy balance in SWAN. By making the mud-adjusted wave number available through the whole code, also influence of fluid mud on energy propagation is included in the model. The performance of the model for both energy dissipation and energy propagation is validated and compared to analytical solutions for some simple cases. Result The final result of this study is a modified version of SWAN which allows to model the decrease of energy during the propagation of a wave field over fluid mud. The model is ready for use in engineering applications by specialists.