The two-dimensional porous medium model (PMM) has been applied to predict the redistribution of protein in the extracapillary space (ECS) of hollow-fibre bioreactors (HFBRs) during open-shell and closed-shell operations. The time-dependent convection-diffusion equation describing protein transport was coupled with the quasi-steady lumen and ECS pressure equations through a relationship between the osmotic pressure and the concentration of protein. Model simulations of closed-shell operation with radial lumen pressure gradients imposed at the inlet and outlet of the fibre bundle showed significant axial as well as radial polarisation of ECS protein. Experiments were carried out to determine the ECS protein distributions that arise during HFBR inoculation. The PMM predictions were generally in better agreement with the experimental data than those obtained using a one-dimensional Krogh cylinder model (KCM). Although the experiments demonstrated significant angular variations of concentration, believed to be due to non-uniform fibre distribution, the angularly and radially averaged concentration profiles were generally well represented by the PMM. Differences between the theoretical and experimental results can be explained by natural convection effects caused by vertical gradients of protein concentration and fluid density.