A hyperelastic constitutive model is implemented to study the formability on three-dimensional complex shapes of a single layer E-glass non-crimp 3D orthogonal woven reinforcement. Experimental measurements of the main deformation modes have been used to identify the strain energy density function of the constitutive model. The comparison of the finite element simulations and experimental results of tetrahedron and double-dome shaping processes demonstrated the adequacy of the adopted hyperelastic model to describe the deformation mechanisms involved during draping and the efficiency to predict the global behaviour of the non-crimp 3D woven reinforcement during complex shape forming. (C) 2015 Elsevier Ltd. All rights reserved.