The determination of the mechanical properties of fabrics in biaxial tension and in-plane shearing is made from 3D finite element analyses of the unit woven cell. Compared to experimental tests these virtual tests have several advantages. They can easily be carried out for sets of varied parameters, they provide local information inside the woven material and above all they can be performed on woven materials that have not yet been manufactured. The 3D computations are not classical analyses because the yarns are made up of several thousands of fibres and their mechanical behaviour is very special. Several specific aspects of the analysis are detailed, especially the use of a hypoelastic law based on an objective derivative using the rotation of the fibre which allows a strict evolution of the directions of orthotropy according to the fibre direction. Examples of analyses are presented in biaxial tension and in-plane shear for woven reinforcements and in the case of the biaxial tension of a knitted fabric. The results obtained are in good agreement with experimental results.