We consider numerical solution of duct flows of multiple visco-plastic fluids using both regularisation techniques and the augmented Lagrangian method. Using single fluid test problems, we demonstrate that there are certain classes of problems for which the augmented Lagrangian method is superior. These problems include those ofdetermining the critical Bingham numbers and pressure gradients for which the flow stops, i.e. the yield limit. We then apply this method to two practical problems involving multiple fluids in ducts: multi-layer lubrication flows and counter-current exchange flows. Again we demonstrate the effectiveness of the augmented Lagrangian method for this type of problem. (C) 2004 Elsevier B.V. All right reserved.