The internal mechanisms of expression operations are analysed in view of the variations of flow rate through filter-cake and of the modified consolidation coefficient through consolidated cake, and basic equations for consolidation processes are presented in this paper. Expression operations are classified into three types according to the relations of pressure and flow rate to time. The equations for flow variations in filter-cakes are numerically solved on the basis of the so-called modern filtration theory. The generalized basic equations for consolidation are solved by using the calculus of finite difference with variable coefficients. It has been demonstrated that the operational variables for expression operations can be more reasonably determined from calculations based upon these numerical solutions rather than predicted by the approximate methods formerly reported. Favourable coincidence between theory and experiments are assured under constant pressure, constant rate and variable pressure-variable rate conditions.