The present paper is devoted to the research of a spatially one-dimensional model of flocculated suspensions in the clarifier–thickener. This model unites a theory of sedimentation– consolidation processes of flocculated suspensions, which leads to a strongly degenerate diffusion equation, with the discontinuous flux. The development of steady-state concentration pro- files in a continuously operated clarifier-thickener is described. Numerical examples for construction of steady-state profiles and their applications for comparisons different modes of operation, to the control of sediment height are presented.