Through the international corporative benchmark works, the material characterization of the woven fabric composites has been examined to better understand their mechanical properties and to provide the process design information for numerical analysis. As the second stage of the benchmark work, the double-dome geometry has been used to illustrate the effect of numerical schemes on the forming behaviors of the woven composites parts. To account for the change of fiber orientation under the large deformation, the non-orthogonal constitutive model was utilized and nonlinear friction behavior was incorporated in the simulation. The equivalent material properties based on the contact status were used for the thermo-stamping process. Furthermore, we incorporated a recently developed non-orthogonal model which captures the dependency of shear behavior of woven fabric composites on the tensions in yarns. Simulation results showed the effect of coupling on the predicted forming behavior for the double-dome parts. As numerical results, blank draw-in, punch force history and fiber orientation after forming have been compared based on various numerical models and methods.