The Kynch theorem was extended to non-linear system of conservation laws of polydisperse suspensions of spherical particles. The simulation predicts overflow of light particles and heavy particles at steady state and dynamic mode of batch and continuous sedimentation. The model eliminated the need for imposed non-theoretical parameters or functions to predict hindered settling and effluent concentrations. Particle-size distribution is also predicted at the effluent and the underflow. We examined several cases and predicted dynamic behaviour of rarefaction waves and overloaded continuous settler. A new concept of dynamic flux curves is also used and introduced. (C) 2004 Published by Elsevier Ltd.