A set of three-dimensional failure criteria for laminated fiber-reinforced composites, denoted LaRC04, is proposed. The criteria are based on physical models for each failure mode and take into consideration non-linear matrix shear behaviour. The model for matrix compressive failure is based on the Mohr-Coulomb criterion and it predicts the fracture angle. Fiber kinking is triggered by an initial fiber misalignment angle and by the rotation of the fibers during compressive loading. The plane of fiber kinking is predicted by the model. LaRC04 consists of 6 expressions that can be used directly for design purposes. Several applications involving a broad range of load combinations are presented and compared to experimental data and other existing criteria. Predictions using LaRC04 correlate well with the experimental data, arguably better than most existing criteria. The good correlation seems to be attributable to the physical soundness of the underlying failure models. Pinho, Silvestre T. and Davila, C. G. and Camanho, P. P. and Iannucci, L. and Robinson, P. Langley Research Center NASA/TM-2005-213530, L-19089 FAILURE MODES; MATHEMATICAL MODELS; NONLINEARITY; SHEAR STRESS; THREE DIMENSIONAL MODELS; MECHANICAL PROPERTIES; FIBER COMPOSITES; FINITE ELEMENT METHOD; PLANE STRESS; COMPRESSIBILITY; FRACTURE MECHANICS; KINKING; STRESS DISTRIBUTION