In this study, a meso-scale finite element (FE) model of a triaxial braided composite is generated based on realistic unit cell dimensions and fiber bundle geometry parameters. Micromechanical finite element models were developed to predict the elastic and strength properties of each fiber bundle. These details are then applied in a 14 unit cells meso-mechanical finite element model for a 0°/+60°/−60° triaxially braided T700s/E862 carbon/epoxy composite. Simulations of the axial tension and transverse tension response of a straight-sided, single layer coupon are conducted using this meso-scale model, and the predictions are compared to experimental results. By applying a periodic boundary condition in the loading direction and an accurate number of unit cells perpendicular to the free edge, the meso-scale model captures the local damage initiation and global failure behavior, as well as the periodic free edge distortion effect. The failure mechanisms are studied using the field strain and stress contours.