A finite element made of woven unit cells under biaxial tension and in-plane shear is proposed for the simulation of fabric forming. The simulation is made within an explicit dynamic approach and is based on a simplified dynamic equation accounting for tension and in-plane shear strain energy. The biaxial tensile properties (given by two surfaces) and the in-plane shear properties (given by a curve) can be determined both by biaxial tensile tests and picture frame experiments or obtained by mesoscopic 3D finite element analyses of the woven unit cell. The interior load components of the proposed finite element are calculated explicitly and simply from the tensions and shear torque on four woven cells. The results obtained by the simulations of a hemispherical forming process on a very unbalanced fabric are compared to experiments. It is shown that the tension strain energy permits to describe the asymmetry of the response but that the computation of wrinkles and of the deformed states when the locking angle is exceeded needs to take the in-plane shear stiffness and its evolution with shear angle into account.