Abstract: Failure criteria for isotropic and anisotropic materials are briefly reviewed.They serve as a background for the criterion presented below.Based on the work of Reference 1and 5,a failure theory which is predominted by matrix and interface failure is presented to predict the failure of composite materials under complex stress state.The criterion formula greatly depends on the failure characteristics of the matrix,while coefficients test of the formula are entirely determined by the properties and volume fraction of the components and the adhesion of interface.The theory also exposes how these parameters influence the failure of the materials,which is significant for material and structure design of composites. The theoretical predictions of off-axis tensile strength agree well with experimental results.