Simulations of composite reinforcements draping use shell finite elements for which the bending behaviour is very particular. The fibrous composition of the reinforcements significantly reduces the bending stiffness compared to classical materials. Moreover, the kinematics of the deformation is strongly modified and does not follow classical theories such as Kirchhoff's. The objective of this paper is to show that a fibrous shell approach based on the quasi-inextensibility of the fibres makes it possible to correctly model the deformation during forming. In particular, the rotation of the material normal is simulated in good agreement with the forming experiments, which is not the case for the alternative approaches that have been proposed for the draping of composites.