The global behavior of sedimenting monodisperse suspensions of rigid spheres can be deduced from the flux plot, but this approach is not available for polydisperse suspensions. The rapid increase in computing power has made simulation an attractive method. Sedimentation of suspensions with many species can now be handled easily. Two sources of difficulty, generation of a concentration gradient and control of fluctuations in concentration, can be overcome by choosing the controlling concentration as that immediately below the test sphere. Applied to randomly distributed particles, our deterministic algorithm yields the ensemble behavior of each species and prepares the way for stochastic simulations by correcting density inversions. The simplicity and generality of the method make it feasible to test any theoretical or empirical model against any experimental data. Simulating the experiments and comparing the simulated and experimental results is illustrated. (c) 2005 American Institute of Chemical Engineers.