Abstract: In order to reveal the influence mechanism of braided structure on the mechanical properties of multi-axial non-buckling fabric (NCF) composites, this paper proposes a NCF structure description and simulation modeling method with in-plane ripple ratio as a unified characterization parameter. The influence of braided structure parameters on the geometric morphology of fibers is equivalent to the in-plane ripple of fibers, which realizes the unified description and prediction of the structure and properties of NCF composites, and systematically analyzes the influence of braided structure on its tensile, compressive and damage evolution behavior. Based on the structural parameters of three kinds of NCF fabrics obtained by Micro-CT characterization, a high-fidelity modeling method considering the change of fiber bundle cross-section was established, and NCF composite models with in-plane ripple ratios of 0.032, 0.037 and 0.042 were constructed. Combined with the three-dimensional Hashin failure criterion, the tensile and compressive mechanical responses were numerically simulated. The results show that the prediction errors of tensile and compressive strength are less than 8 %, which are in good agreement with the experimental results. At the same time, the crack path is in good agreement with the fracture morphology of the experimental test, which verifies the effectiveness of the proposed structural description and simulation modeling framework. The parameter sensitivity shows that with the increase of the corrugation ratio, the tensile and compressive strength of the composites show a significant downward trend, and the compression performance is more sensitive to the corrugation. Further damage evolution analysis reveals that the increase of the in-plane waviness ratio will promote the transformation of the internal damage of the material from dispersed expansion to local instability, and the cracks are more likely to initiate and propagate in advance at the geometric defects of the waviness, accelerating the degradation of the macroscopic bearing capacity. This paper provides a new analysis idea for the structural design and performance optimization of multi-axial non-buckling fabric composites from the aspects of geometric equivalent characterization, mesoscopic modeling and quantitative damage mechanism.