Woven fabrics have been applied widely to many structures. There are many requirements that need to analyze at the micro level. In order to investigate the behavior of the fibers of woven structures at the micro level, a new computational method that the mechanical behavior of composite materials with a large-scale difference can simulate have to develop. Therefore, we have proposed FEM with mesh superposition in 3 scales, and we have defined the new numerical technology as 'M-cube (Macro-Meso-Micro) method. In addition, the method has been expanded with elastic-plastic and damage mechanics to investigate the propagations of transverse crack in fiber bundles as an initial damage mode. The numerical results will give very important information to evaluate the safety of composite structures.