Simulations of 3D textile composite reinforcement deformations performed using classical hexahedral finite elements with displacement degrees of freedom and an appropriate three-dimensional hyperelastic constitutive law reveal some discrepancies with respect to conducted experiments. The inability of the 3D continuous model to take into account the local stiffness of the fibers can be highlighted. An improved modeling approach is proposed by including additional curvature-related internal loads in the 3D element. The approach, based on a rotation free formulation, is efficient. The enhancement is shown in the case of a three point bending test and a hemispherical forming process. (C) 2015 Elsevier Ltd. All rights reserved.