Abstract The objective of this study was to characterize the quasi-static and dynamic behavior of composite materials and develop/expand failure theories to describe static and dynamic failure under multi-axial states of stress. A unidirectional carbon/epoxy material was investigated. Multi-axial experiments were conducted at three strain rates, quasi-static, intermediate and high, 10−4, 1 and 180–400 s−1, respectively, using off-axis specimens to produce stress states combining transverse normal and in-plane shear stresses. A Hopkinson bar apparatus and off-axis specimens loaded in this system were used for multi-axial characterization of the material at high strain rates. Stress–strain curves were obtained at the three strain rates mentioned. The measured strengths were evaluated based on classical failure criteria, (maximum stress, maximum strain, Tsai–Hill, Tsai–Wu, and failure mode based and partially interactive criteria (Hashin–Rotem, Sun, and Daniel). The latter (NU theory) is primarily applicable to interfiber/interlaminar failure for stress states including transverse normal and in-plane shear stresses. The NU theory was expressed in terms of three subcriteria and presented as a single normalized (master) failure envelope including strain rate effects. The NU theory was shown to be in excellent agreement with experimental results.