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. The materials investigated were carbon/epoxy and glass/vinyl ester composites. Multi-axial static and dynamic experiments were conducted 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 above materials at high strain rates. Dynamic stress-strain curves were obtained for the two materials mentioned before and compared with corresponding static ones. The results obtained were evaluated based on classical failure criteria, noninteractive criteria (maximum stress, maximum strain), fully interactive criteria (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 and is expressed in the form of three subcriteria. Quasi-static and dynamic failure envelopes were obtained by the various available failure theories including the NU theory and compared with experimental results. The NU theory was extended to the dynamic loading regime and was shown to be in excellent agreement with experimental results.