A finite element simulation of the mechanical behaviour of woven textile materials at the scale of individual fibers is proposed in this paper. The aim of the simulation is to understand and identify phenomena involved at different scales in such materials. The approach considers small patches of woven textile materials as collections of fibers. Fibers are modelled by 3D beam elements, and contact-friction interactions are considered between them. An original method for the detection of contacts, and the use of efficient algorithms to solve the nonlinearities of the problem, allow to handle patches made of few hundreds of fibers. The computation of the unknown initial configuration of the woven structure is carried out by simulating the weaving process. Various loading cases can then be applied to the studied patches to identify their mechanical characteristics. To approach the mesoscopic behaviour of yarns, 3D strains are calculated at the scale of yarns, as post-processing. These strains display strong inhomogeinities, which raises the question of using continuous models at the scale of yarns.