A stress resultant shell approach is proposed to simulate the draping of textile composite reinforcements with continuous fibers. This approach naturally makes it possible to take into account the specificity of the deformation of the fibrous reinforcements by considering independent bending and tension stiffness whereas they are linked in standard shell elements. The stress resultants and stress moments are related to membrane strains and curvatures by rate constitutive equations (hypoelastic laws). The experimental tests required to identify the material properties necessary for these constitutive laws in stress resultants are presented. This approach is implemented in the ABAQUS finite element code and can be used by all users of this software. A set of forming tests showed the effectiveness of the approach through comparisons between simulation and experimental results.