Today, numerical simulations of shaping fibrous reinforcements are based on continuous material models that have been assumed to be nonlinear elastic thypoelastie [1] or hyperelastic [2, 3]). Nevertheless, it is also believed that during the shaping process, there is a possible non reversibility of behavior that plays a significant role. In this work, we are interested in quantifying the importance of these phenomena by doing a group of tests (flexion, shear, compression) and then afterwards by proposing models compatible with the simulation of industrial parts when irreversibility is significant.