The mechanical behavior of a four-layer plain weave glass fiber/epoxy matrix composite is modeled at the mesoscopic scale, taking into account the dry fabric preforming before resin injection, the relative shift and nesting between fabric layers, and the characteristic damage mechanisms, i.e., intra-yarn cracking and decohesion at the crack tips. The surface strain fields obtained numerically are similar to the strain fields observed at the surface of the specimen. Damage is modeled by introducing discrete cracks in the FE mesh of the representative unit cell of the composite. The crack locations are determined using a stress based failure criterion. The predicted locations are similar to those observed experimentally. The effects of intra-yarn cracks on the macroscopic mechanical properties show the same trends as the experimental data. Good quantitative agreement is obtained if yarn/yarn or yarn/matrix decohesions at the crack tips are taken into account.