This study presents a numerical model for pressure deliquoring of compressible solids, covering both filtration and expression. A simple and easy-to-solve model for the solid/liquid system is obtained by formulating the basic flux and continuity equations in material coordinates. A precise determination of the flow resistance between the spatial node points in the numerical solution scheme is obtained for even extremely compressible solids by integration of the liquid flux equation with respect to cake thickness. Model calculations show that the extreme compressibility typical for biological solids results in the formation of a skin above the filter medium. This skin becomes limiting to liquid release from the cake during expression. The numerical model for unified filtration and expression seems promising to further improve the understanding and control of dewatering of biological sludges as well as other solid/liquid suspensions.