This article introduces a methodology to measure in-plane permeability of fibrous media using a transient one-dimensional air flow with absolute pressures ranging from 10(3) to 10(5)Pa. The method, based on the measurement of gas pressure at the boundaries throughout the transient flow, is convenient, clean and fast, avoids usage of a gas flow meter and offers a way to study the gas transport within fibrous media. The transport of a compressible fluid is described by several models to comply with different flow regimes which can occur during the experimental measurements. A thermal analysis is given to verify the validity of isothermal conditions during the tests. The permeability, only depending on the fibrous structure, is determined by inverse method, fitting the simulation results to the experimental data obtained using raising or dropping pressure methods. The deviation from Darcy's law caused by gas sliding effect is analysed and a relative parameter of fabric material shows a dependence in permeability, with a similar trend as the Klinkenberg sliding parameter in soils and rocks.