A non-idealized finite element model of a plain orthogonally woven textile composite was subjected to tension along the warp direction, and the predicted stress state was investigated. The effect of refining the geometry and mesh on the volume average stresses and the percentage of each constituent at different stress levels was explored. For the particular textile architecture considered, which consisted of large reinforcement tows and complex tow cross sections, it was shown that the typical mesh refinement in the literature might suffice for volume average stresses, but a higher mesh refinement is needed to accurately capture stress concentrations. The locations of stress concentrations within each constituent were identified. For the three types of tows, [Formula: see text], transverse normal stress in the local coordinate system, in the wefts was predicted to be the most severe component of stress. For the layers of wefts that are crossed over or under by a binder, stress concentrations developed where the warps were the most distorted. Whereas, for the interior layer of wefts, stress concentrations developed where a binder came closest to the weft. In the matrix, [Formula: see text], the normal stress in the direction of the load, concentrations developed where a binder came close to a warp or weft. The locations of peak cross-sectionally averaged stresses along the tow paths were shown to match the locations of local stress concentrations. However, it was observed that many of the stress concentrations might be sensitive to the method used to create the finite element model, boundary conditions, or accounting for the variation of local fiber-volume fraction that results from a variation of cross-sectional area.