In a first fine dispersed suspension filtration stage a compressible filter cake builds up. The subsequent cake consolidation is applied to reduce the liquid amount in the small pores of the cake. To describe the two-stage expression process of fine sludge a new model is introduced. In contrast to the conventional TILLER-SHIRATO model which assumes constant average material properties of particle pressure p(s), packing density epsilon(s) and permeability k inside the cake during constant pressure expression. the new expression model considers the process dynamics, i.e. time and space dependent variation of these material properties. Furthermore the wall friction angle phi(w) and the lateral pressure ratio lambda of the cake at the wall is taken into account. To measure the most important process parameters, a new test apparatus called a press shear cell is introduced that is a combination of a pressure filter, a modified compression permeability cell and a ring shear cell. The pressure dependent material functions of kaolin and titanium dioxide filter cakes are shown. If a filter cake in thin layers is produced the wall friction in the press shear cell can be neglected and a model comparison of both models with expression tests is presented.