The inability of the model of Cauchy to describe, during a fibrous reinforcement forming, both the possibility of slippage between the fibres and the bending stiffness of the fibres is highlighted. An approach is proposed to overcome these difficulties and to model the mechanical behavior of fibrous reinforcements taking into account the local fibre bending stiffness. A stiffness related to the curvature is added to hexahedral finite elements. For this, the positions of neighboring elements are used to calculate the curvature in the element. In both cases, the local fibre stiffness is taken into account without modifying the weak shear stiffness.