In most cases, fibrous composite reinforcements can be modeled as a continuum medium. Nevertheless, it is shown on some examples that the models in the standard continuum mechanics of Cauchy are not able to correctly describe the mechanical behavior of fibrous reinforcements. The reasons for these difficulties are analyzed thanks to a very simplified model. The inability of the model of Cauchy to describe both the possibility of slippage between the fibres and the bending stiffness of the fibres is highlighted. Two approaches are proposed to overcome these difficulties and to model the mechanical behavior of fibrous reinforcements taking into account the local fibre bending stiffness. First, the continuum model is completed by a generalized second gradient continuum theory. An alternative solution is to add a stiffness related to the curvature 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.