PURPOSES : The wedge-type anchorage system requires a complex analysis of not only the tensile stress of the CFRP plate, but also the compressive stress and shear stress generated by the wedge action. The purpose of this study is to find a composite material failure theory that is suitable for analyzing the behavior of wedge-type anchorage system among various failure theories. METHODS : In this study, numerical analysis of various composite material failure theories was performed to analyze the anchorage strength and failure mode of the wedge-type anchorage system according to each failure theory, and compared with actual test results to determine the composite material failure theory most suitable for analyzing the behavior of a wedge-type anchorage system. RESULTS : Since the Maximum Stress failure theory shows similar results to the actual test in terms of failure mode and anchorage strength, there is no significant problem in applying it to the wedge-type anchorage system. However, it is judged to be difficult to apply under property conditions where interactions between stresses are highlighted. The Tsai-Hill and Tsai-Wu failure theories are considered unsuitable for application to wedge-type anchorage systems because the wedge angle conditions at which the most advantageous anchorage strength occurs are significantly different from other theories and the fracture type cannot be predicted. The Hashin-Rotem failure theory is considered to be the most appropriate to apply as a failure theory for the wedge-shaped anchorage system because the anchorage strength was slightly lower than the actual test results, but there was no significant difference, and the failure mode was consistent with the test results. The Hashin failure theory is judged to be unsuitable for application as a failure theory for the wedge-type anchorage system because the anchorage strength and failure mode were interpreted differently from the actual test results. CONCLUSIONS : The Hashin-Rotem failure theory was presented as the composite material failure theory most suitable for analyzing the behavior of wedge-type anchorage system.