Washers units are used in a wide range of continuous sedimentation and sludge thickening processes where solid particles from continuous inflow mixtures are separated from the liquid. In this operation, solids concentration increases by settling, and the formation of a thicker bed is inevitable with time. Under optimal operating conditions, it is always possible to obtain two discharges from those vessels: a highly concentrated suspension at the bottom (underflow), and a clarified liquid stream at the top of the equipment (overflow). In the Bayer Process an insoluble sub-product is formed as a result of the digestion of the Bauxite ore with Caustic Soda. It is called “Red Mud”, and it has to be continuously washed by settlers. This process is carried out on trains of washers using counter-current decantation. This method has been used for about a century. However, its performance is difficult to model and predict due to its highly nonlinear behaviour. This paper proposes a dynamic solution for the process described above. It basically involves the reliable development of a non linear model, which will be used as a tool for predicting the optimum performance of a red mud washer. The simulation of the thickening process is carried out by applying a kinematic sedimentation model extended to flocculated suspensions which leads to a scalar nonlinear conservation law. The approach uses a conservative finite difference scheme of upwind type for solving an initial-boundary value problem, which is the main characteristic of strong nonlinear convection-diffusion equations.