The concept of standing concentration waves is introduced to derive design equations for continuous moving bed (CMB) processes. For linear isotherm systems, simple equations are derived from the analysis to link product purity and recovery to zone lengths, bed movement velocity, flow rates, column capacity factors, and mass-transfer coefficients. Once product purity, recovery and feed flow rate are specified for a given system, the zone flow rates and bed movement velocity that provide the highest throughput and the lowest solvent consumption can be determined from the solutions. In a given system, there is a trade-off between product purity and throughput. If bed volume and product purities are fixed, the longer the zone lengths, the higher the throughput. Simulations based on a linear driving force model that considers axial dispersion and lumped film and intraparticle diffusion are used to compare the column profiles and effluent histories of CMB and simulated moving bed (SMB). A numerical algorithm is introduced to allow simulation of both CMB and SMB operations using the same program. The comparison shows that the design equations derived for CMB systems are applicable to SMB systems. Finally, the standing wave solutions are used to analyze an experimental SMB system from the literature (Ching et al., 1991). Simulations agree closely with the data and the predictions of the theoretical analysis.