We propose a new modeling strategy based on hybrid elements for virtual fiber modeling (also known as the digital element method) to predict both kinematics as well as mechanics of woven fabrics. In virtual fiber modeling, yarns are modeled consisting of a number of discrete fibers. We show that through the development of a modeling strategy based on hybrid elements, we are able to impose correct properties in the fiber direction, as well as out-of-plane properties thanks to the inclusion of fiber bending stiffness. This approach accurately predicts the through thickness compression of a 2x2 twill glass fiber woven fabric. Both kinematically, as well as mechanically, good agreement between experiment and simulation is obtained. Ultimately, these kinds of models could allow faster virtual prototyping as the amount of experimental input is very low and can usually be found in the datasheet. @en