This work details the one-dimensional modeling of the different processes that may occur during the vacuum filtration of compressible flocculated suspensions. Depending on the operating conditions of the applied pressure and the initial solids concentration relative to the material properties of the compressive yield stress and the effective capillary pressure at the air-liquid interface, the dewatering process undergoes a combination of cake formation, consolidation, and/or desaturation. Mathematical models for these processes based on the compressional rheology approach are presented and appropriate solution methods outlined. Results using customary material properties are given for different operating conditions to illustrate the three dewatering processes. This approach lays the theoretical basis for further work understanding two-and three-dimensional effects during desaturation, such as cracking and wall detachment. (C) 2010 American Institute of Chemical Engineers AIChE J, 56: 2622-2631, 2010