A model for the dynamic behaviour of the wet front radius and the liquid saturation in a capillary suction apparatus (CSA) is developed. Governing equations based on mass/momentum balance are derived and solved numerically. The calculation shows that the effects of the initial conditions on system dynamics vanish rapidly, and that the system then evolves along a slow manifold which is independent of the initial conditions chosen. It is also noted that, after sufficient time, the log-log plot of the dimensionless wet front radius versus dimensionless time can be approximated by straight lines and the liquid saturation under the inner cylinder can be taken as constant with error less than 5 %. The increase in solids concentration and/or the averaged specific resistance of cake increases the capillary suction time (CST) significantly. The proper range of experimental conditions is suggested. A rapid method based on the model for estimating the averaged specific resistance of cake is proposed and compared with experimental results.