In this paper, the general multimaterial formulation of Kashiwa and Rauenzahn [1] is used to derive an appropriate hydrodynamic model for a trickle-bed reactor operating under trickling flow conditions. Using some realistic assumptions, the resulting model consists of two equations in two unknowns, i.e.. liquid volume fraction and pressure. Moreover, the equations exhibit elliptic (pressure) and hyperbolic (volume fraction) behaviours, which require the use of different numerical methods in order to correctly handle these different numerical behaviours. Thus, the finite volume method. the Crank-Nicholson scheme and the second order Godunov's method combined with the solution of Riemann problem were implemented. The numerical results of pressure drops derived from the model solution are shown to be in good agreement with the values measured in the same operating conditions or previously published in the literature. (c) 2004 Elsevier B.V. All rights reserved.