Mesoscopic simulations of the transverse compression of textile preforms are presented in this paper. They are based on 3D FE models of each yarn in contact with friction with its neighbours. 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. 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.