As textile materials are increasingly used as reinforcements in composites structures, their mechanical properties need to be better identified, both at macroscopic scale to estimate for instance their formability and at the microscopic scale to predict breaking of fibers. The mechanical behaviour of such materials is made complex by contact-friction interactions taking place between their components of different levels. For woven materials, that are made of interlaced tows, interactions occur both at a mesoscopic scale between tows and at a microscopic scale between fibers constituting the tows. The approach proposed to identify mechanical properties of such materials is based on the finite element simulation at the scale of individual fibers. Small samples of fibrous structures are considered, taking into account all fibers. The global mechanical problem is set in the form of seeking the equilibrium for a general assembly of fibers undergoing large displacements and finite strains, and generating contact-friction interactions between them. An implicit solver is used, allowing to handle large loading increments. A special care is given to the consideration of the numerous contact-friction interactions occuring between fibers. Zones of proximity between fibers are first delimited within the assembly. Intermediate geometries aimed at approximating the actual geometry of contact zones are then defined and used as geometrical support to generate contact elements, constituted by pairs of material particles predicted to enter into contact. An adaptive and regularized penalty method is employed to model the normal behavior of contact elements, and a regularized Coulomb's law is considered for friction. To simulate the behaviour of different kinds of fibrous structures, a versatile driving of boundary conditions has been developed. Rigid bodies are introduced in the model so that global displacements or forces can be applied to sets of fiber ends. Forces and displacements are prescribed to the rigid bodies while fiber ends are bound to them through average conditions. This allows to maintain globally sets of fibers ends, while leaving them rearrange. In the case of woven fabrics, as the initial configuration of fibers cannot be known a priori, the simulation code is used to compute the initial geometry of small woven samples, by making yarns gradually fulfill the stacking order defined by the weaving pattern through the consideration of proper contact conditions. Once the initial configuration has been computed, various loadings can be applied to identify the mechanical behaviour corresponding to different deformation modes. The identification of individual tow mechanical properties is also important to understand the global behaviour of woven fabrics. To this end, crushing tests on individual yarns under tensile loadings are simulated to highlight coupling effects between loadings in different directions. The presented tests illustrate the ability of the approach to handle problems involving few hundreds of fibers submitted to various loadings, in order to investigate the global behaviour of fibrous materials.