The permeability prediction of real fibrous media remains a major challenge due to their complex porous structure. The existing models generally take two parameters into account that depict the average structural properties of fibrous media: porosity (or solid volume fraction) and fibre diameter (or radius). Due to the local variations that those parameters can exhibit the models often fail to accurately predict the permeability. In this study experimental data of three fibrous media of different porous structures employed in air filtration are used to assess numerous empirical and analytical models from the literature. It is found that all the models considered significantly under-predict the experimental permeability values. Special attention is given to the analytical Representative Unit Cell (RUC) model which is physically adaptable and can therefore be used to investigate the aforementioned discrepancies between model and experiment. Local porosity variations are investigated through a sensitivity analysis on the minimum and maximum solid volume fraction values. Incorporation of the porosity variations into the RUC model significantly reduces its under-prediction and may also serve as explanation for the discrepancies observed. An adaptation to the RUC model is proposed that takes into account the anisotropy effects as a result of the stacking of fibrous medium sheets into several layers and the increase in porosity as a result thereof. The adapted analytical model gives an indication on the factor to apply on the mean porosity in order to incorporate the anisotropy effect into the model prediction, and so reduce the observed under-predictions. (C) 2018 Elsevier Ltd. All rights reserved.