Thermostructural woven composite materials are receiving particular attention in a wide range of specialized aeronautical applications. Reliable numerical prediction tools based on both geometrical and mechanical modeling are required to quantitatively characterize the role of the microstructure and damage mechanisms at the mesoscale. In this paper, a finite element strategy is proposed illustrating a generic two-dimensional repeating unit cell of a SiC/SiC plain weave composite with chemical vapor infiltrated matrix. Tows damage mechanisms are introduced through a nonlinear model based on damage mechanics as well as homogenization of a micromechanical model on the fiber scale. Particular attention is paid to the generation of accurate hexahedral meshes, compatible at the tow-tow and tow-matrix interfaces. The mesh quality is verified using an error estimator variable based on the strain energy density. Intra-yarn damage prediction obtained using tetrahedral and hexahedral elements is tested and compared considering the representative unit cell subjected to tensile loading.