For several membrane separation processes, hollow fibre modules are either an already established or a promising type of module. Based on the analogy between mass and heat transfer, an engineering approach is proposed to estimate the shell-side mass transfer coefficient for axial flow in hollow fibre modules with due allowance for the void fraction. The approach enables one to take the entrance effects of the hydrodynamic and concentration profile into account. The trends obtained by this generalised approach are similar to those of empirical correlations found in the literature over a wide range of Reynolds numbers and module packing densities. The empirical correlations differ significantly one from the other. The differences between the mass transfer coefficients obtained by the empirical correlations compared to those obtained following the approach proposed in this study are discussed. The different effects influencing mass transfer in hollow fibre modules are identified and discussed as a function of void fraction. Further, an approach to reflect the influence of maldistribution on mass transfer performance is provided.