In this study a geometric anisotropic two-strut model is presented to predict the permeability of fibrous porous media subject to compression. A further novelty of this study is the inclusion of the Klinkenberg effect in the permeability prediction of the two-strut model and existing three-strut model. The specific surface area of the anisotropic models are predicted by making use of two approaches, i.e. a geometric approach and a combined kinematic-geometric approach. The Klinkenberg effect has also been introduced into the non-compressed models. The model predictions are compared to a variety of available experimental data for non-woven fibre media and metal foams from the literature and the correspondence proves to be satisfactory. The analytical modelling approach presented adds value to the empirical studies in the literature which comprises of curve fitting procedures together with the introduction of empirical coefficients into the Forchheimer or Ergun equations to obtain correlation with experimental data. (C) 2020 Published by Elsevier B.V.