To assess the safety of navigation in muddy areas, a comprehensive captive manoeuvring model test program was executed. Based on the results of this experimental program, a four-quadrant manoeuvring model was built with a separate set of coefficients for each combination of under-keel clearance and mud layer characteristics. The disadvantage of this model is that only conditions corresponding with the experimental ones can be simulated. A more consolidated mathematical model was needed. This was achieved with the introduction of a fluidization parameter that determines the corresponding hydrodynamically equivalent depth above a solid bottom. As a result, the under-keel clearance dependency of a given mathematical manoeuvring model can be reformulated in such way that the effect of any realistic muddy condition is included. In this article, the modelling of the hull forces, the propeller thrust and torque, and the forces acting on the rudder will be discussed.