A two-step methodology is proposed in order to estimate from numerical simulations the permeability of deformed woven fabrics. Firstly, the shear deformation of a glass plain weave until the shear locking is studied from a mesoscale analysis achieved with a representative volume element (RVE) of the periodic plain weave. Simulations have been carried out within the scope of large transformations, accounting for yarn–yarn contacts, and assuming that yarns behave as hypoelastic materials with transverse isotropy. From the simulated deformed solid RVE, a complementary periodic fluid RVE is then built and the slow flow of an incompressible Newtonian fluid within it is investigated. This allows to compute, in a second step, the permeability of the deformed plain weave. The role of the shear deformation on the permeability of multi-layers or single layer preforms is discussed.