The mechanical properties of triaxially braided composites under transverse loads are found to be size-dependent, due to the presence of free-edge effect. Numerical studies of the mechanical behaviors of straight-sided coupon specimens and an infinitely large plate under both axial and transverse tension loads were conducted using a meso-scale finite element model. The numerical model correlates well with experimental results, successfully capturing the free-edge warping phenomena under transverse tension. Free-edge effect is observed as out-of-plane warping, and it can be correlated to the premature damage initiation in the affected area. The numerical results characterize the impact of free-edge effects on the global stress-strain response and local failure mechanisms. By conducting dimensional analysis, the relationships of effective stiffness and strength against specimen width are quantified using Weibull equations. The results of this study indicate that the free-edge effect is an inherent behavior of braided architecture. The free-edge effect produces significantly reduced transverse tension modulus and strength measurements.