The concept of a particle concentration dependent yield stress, previously employed in studies of uniaxial consolidation of a flocculated solid phase dispersed in a liquid, is extended to comprise flocculated phase shear strength. The inter-particle stresses are modeled by assuming that the stress state is always located on a yield-surface in stress-space, whose form is adopted from the Cam-clay plasticity theory for the quasistatic consolidation of soil. By treating the time-dependent dewatering of a suspension trapped between a permeable filter and a sliding piston, as well as the asymptotic limit of a cross-flow filtration situation, the differences with respect to the conventional uniaxial models are made apparent, and the effects of the shear stresses on the consolidation process are elucidated. Applying shear is predicted to increase the rate of the drainage process, because of a reduced load bearing capacity of the flocculated phase, and the correspondingly higher pore pressures. (c) 2008 American Institute of Chemical Engineers.