A finite element simulation of composite woven reinforcement forming requires the knowledge of the fabric mechanical behaviour. In the presented mesoscopic approach, the tensile and shear mechanical behaviour of the elementary cell (mesoscopic level) are used in a finite element made of woven meshes. The principal stiffness of the fabric is the tensile rigidity. Because of the weaving, the tensile behaviour is non-linear. It is analysed by biaxial tensile tests and 3D finite element computations of the woven unit cells. The in plane shear rigidity of fabrics is very weak up to a limit angle. In this first stage, it is shown by optical measures that the yarns are subjected to rigid rotations. A second stage in which the yarns are laterally crushed leads to larger stiffness. A first simplified form of the dynamic equation is based only on tensile internal virtual work. A second one takes also shear internal work into account. A fabric square box forming simulation is performed with both approaches. It shows the importance to account for shear when the limit shear angle is exceeded.