A new model of hollow-fibre membrane devices has been developed in which the lumen and shell sides of the fibre bundle are treated as two interpenetrating porous regions. Darcy’s law and fluid continuity are combined to give a set of two-dimensional partial differential equations governing the hydrodynamics within these devices. The computational domain corresponds to the real dimensions of a hollow-fibre cartridge and hence macroscopic radial gradients, which exist during some operations, can be taken into account. The effects of fibre expansion under wet conditions are also included. The model was used to analyse fluid flow in several different configurations, including the closed-shell mode, dead-end and cross-flow filtration as well as counter-current and co-current contacting. The effects of the membrane and shell-side hydraulic permeabilities on the volumetric flow rates and spatial flow distribution were investigated and the predictions were compared with those of one-dimensional models based on the Krogh cylinder approximation. The new model can be readily extended to incorporate solute transport, gravitational effects, non-idealities of cartridge design or local variations of system parameters.