Transverse compaction of textile composite reinforcements is an important deformation mode arising during composite forming and manufacture. The mesoscopic simulations of the transverse compression of textile preforms presented in this paper are based on 3D FE models of each yarn in contact with friction with its neighbours. A hypoelastic model based on the fibre rotation depicts the mechanical behaviour of the yarn. The compression responses of several layer stacks with parallel or different orientations are computed. The numerical simulations show good agreement when compared to compaction experiments. The mesoscopic simulations can be used as virtual compression tests. In addition they determine the internal geometry of the reinforcement after compaction. The internal geometry can be used to compute the permeability of the deformed reinforcement and to calculate the homogenised mechanical properties of the final composite part."