Kynch's theory of sedimentation is adopted to solve for the attainable steady state concentration in a vertical continuous sedimentation basin incorporating a thickener and a clarifier. The limiting flux solution corresponding to the local minimum at the flux concentration curve is proved to have a limited range of validity and is shown to apply only to the intermediate range of feed concentrations. This limit is replaced by a five‐region diagram; the solution is determined by the feed coordinates in the flux concentration plane, with respect to the flux concentration curve. Each section exhibits different characteristic solutions for both the clarifier and the thickener. The analysis, which combines dispersion, dynamics, and stability considerations, reveals new possible ranges of operating conditions where the flux exceeds the limiting flux and solids are not entrained. The results, contradicting previous published work, are verified by a finite‐difference dynamic simulator.