The presence of mud layers on the bottom of ports and waterways can have negative effects on the hydrodynamic behaviour of marine vessels. This numerical study investigates the effect of muddy seabeds on the full-scale resistance of an oil tanker sailing straight ahead. The objective is to determine the influence of factors such as the densimetric Froude number, UKC and mud rheology at speeds between 3 and 9 knots. The numerical study is conducted using a finite-volume Reynolds-Averaged Navier–Stokes (RANS) flow solver combined with the Volume-Of-Fluid (VOF) method to capture the mud–water interface. At certain critical speeds, the presence of mud increased the ship’s total resistance by up to 15 times compared to the case with solid bottoms. The non-Newtonian rheology of mud was found to influence the ship’s resistance mainly at low speeds and when sailing through the mud layer. This article also shows that, when sailing through mud, the computed resistance at high speeds may be underestimated because of two effects, namely ‘water lubrication’ and ‘numerical ventilation’. •Effect of mud on the resistance of KVLCC2 is numerically investigated.•CFD simulations are performed using a finite-volume RANS flow solver.•Mud is modelled both as Newtonian and non-Newtonian (Bingham) fluid.•Resistance is influenced by internal waves at critical speeds.•Resistance is influenced by mud rheology when sailing through mud at low speeds.