An unsteady state hydrodynamic model is developed to study the transient behaviour of particles and liquid in a continuous liquid-solid classifier by adding transient terms to the steady state hydrodynamic model proposed by Chen et al. (in: M. Kwauk, J. Li, W.-C, Yang (Eds.), Fluidization X. United Engineering Foundation, New York, 2001, pp. 413-420). The two-step Lax-Wendroff scheme is applied to solve the resulting partial differential equations. The predictions of the dynamic behaviour for step changes of liquid fluidizing velocity, feed velocity and discharge velocity are reasonably consistent with experimental results carried out in a 191 mm diameter column with glass beads and water, involving step changes in feed or discharge conditions.