Compactibility of cakes and sediments is a key factor in the behavior of thickeners, filters, centrifuges and belt presses. Stress applied to cakes decreases porosity and increases resistance to flow. Empirical models presented here represent solidosity (volume fraction of solids) epsilon(s), specific resistance a and permeability K as functions of effective pressure p(s) that are essential to developing mathematical models of thickening, filtration, and centrifugation. As suspensions are flocculated, the resulting aggregates become increasingly fragile and more compactible. Cake behavior undergoes substantial change, until it reaches a point at which increasing pressure unexpectedly no longer affects either % cake solids or filtrate volume vs, time. Traditional formulas for filtrate volume us. rime and average values of alpha, K, and epsilon(s) were modified for highly compactible materials. The average value of a is proportional to the pressure drop across the cake and the average permeability is inversely proportional to Delta p(c) .