A finite-element algorithm is developed to solve the population balance equation that governs steady-state behavior of well-mixed pairtculate systems. Collocation and Galerkin methods ave used to solve several test problems in which aggregation, breakage, nucleation and growth (and combinations of these phenomena) occur. It is shown that the Galerkin method must be used in growth problems to obtain a well-conditioned system. In all the cases investigated; density distributions and their moments are accurately predicted by the method. lit a direct comparison with the discretized population balance (DPB) of Litster er nl. (1995) the finite-element method proves capable of predictions that ale typically two orders of magnitude more accurate than those of the DPB. These results were obtained using smaller systems of equations and with considerably less considerably less computational power.