Several two- and three-dimensional mixed-mode interface failure criteria are proposed for predicting delamination failure in multidirectional, laminate composites. The proposed criteria, based on the stress intensity factors K1, K2, and , as well as the critical interface energy release rate and phase angles ψ and ϕ, are examined using results obtained from Brazilian disk mixed-mode fracture toughness tests. Two material systems are considered. The first contains a delamination along an interface between a unidirectional fabric and a plain woven fabric. The second is composed of a plain woven fabric with fibers oriented in different directions in succeeding plies. The former was manufactured by means of a wet-layup and the latter is a prepreg. Finally, a statistical analysis is carried out to obtain a failure curve or surface with a 10 probability of unexpected failure and a confidence. These curves or surfaces may be used to predict failure of structures containing these laminates and to assist in composite design.