The use in the offshore engineering industry of computational fluid dynamics (CFD) to estimate the hydrodynamic forces due to steady, turbulent currents on offshore structures has so far been rather limited. This is largely due to the uncertainties inherent in obtaining accurate solutions to the governing Navier-Stokes equations, particularly for complex geometries and at high Reynolds numbers. In this study, we assess the contributions to such uncertainties arising from a number of factors. Those include the number of nodes in the computational mesh used to overlay the flow domain, the choice of scheme used to discretize the governing equations, the choice of turbulence model used to close the time-averaged equations, and the assumptions made regarding the state of turbulence in the incident current. The influence of these factors is systematically assessed with respect to the flow around a full-scale mini-TLP. The paper also assesses the influence of the current incidence on the hydrodynamic loads on the same TLP. A previous study by the same authors has suggested the presence of substantial “shielding,” whereby the computed steady-state loading on the TLP was found to be significantly lower than the value recommended by the DNV design code. Computations performed here with the direction of the incident current varied in the range 0–45 deg suggest that the extent of this shielding is significantly diminished at high angles of incidence.