Simple model equations which consider different rate control mechanisms are formulated for fixed bed multicomponent ion exchange processes. Efficient and accurate numerical methods are developed for solving these equations for liquid phase, solid phase or combined phase control. The algorithms are applicable to both ion exchange and liquid adsorption and are shown to be extendable to a general form of isotherms. The accuracy of the numerical algorithm is evidenced by the fact that the asymptotic limiting equilibrium solutions are closely approached as the dimensionless length parameter is increased, regardless of the rate control mechanism. Numerical examples for ion exchange applications are presented. These examples included multicomponent elution and purification problems. The effect of mass transfer resistance was also examined. Other examples examine the validity of a model reduction assumption and the comparison of equilibrium theory with the results obtained using the present finite mass transfer rate model.