The transverse permeability of fibrous reinforcement is one of the critical parameters that govern fabrication efficiency and production quality in several liquid composite molding process variants devised to achieve transverse impregnation of fibrous reinforcements. It is difficult to precisely measure and predict the transverse permeability, because it is simultaneously affected by diverse factors, for example, the geometric features of the test mold, nesting between fabric layers, and flow‐induced compaction of the fiber bed. In this article, the saturated transverse permeability of 2D woven glass fabrics is investigated using information provided by mesostructural geometric models reproducing the real textile architecture. These models are created by micro‐CT aided geometric modeling, a recently proposed technique to analyze three‐dimensional images obtained by X‐ray microtomography. They are called “material twins” because they reproduce with assessed accuracy the geometrical configuration of the textile preform, are representative of material variability, and allow performing numerical simulations of flow or mechanical properties. Computer simulations of steady state transverse flows in material twins were carried out to evaluate the transverse permeability and compared to experiments. Issues concerning material variability due to nesting and the accuracy of transverse permeability measurements were considered and discussed. A good agreement was obtained between numerical and experimental values of transverse permeability. Both approaches show a significant influence of the number of layers considered, which can be explained by nesting between adjacent plies. Numerical simulations also illustrate how nesting significantly affects material variability.