A "mutual integral" approach is used to calculate the mixed-mode stress intensity factors for a free-edge, delamination crack in a laminate under tensile loading conditions. This "mutual integral" approach, for generalized plane strain conditions, is based on. the application of the path-independent J integral to a linear combination of three solutions: one, the problem of the laminate to be solved using the quasi 3-D finite element method, the second, an "auxiliary" solution with a known asymptotic singular solution, and the third, the particular solution due to the out-of-plane loading. A comparison with the exact solutions is made to determine the accuracy and efficiency of this numerical method. With this "mutual integral" approach, it was found that the calculated mixed-mode stress intensity factors of the free-edge delamination crack remain relatively constant as the crack propagates into the laminate. It was also found that the fracture criterion based on the mixed-mode stress intensity factors is more consistent with the experimental observations than the criterion based on the total energy release rate, and hence demonstrates the importance of the ability to calculate each individual component of the stress intensity factors. Furthermore, it was found that the fracture toughness measurements from double cantilever beam specimens can be used directly to predict the onset of delamination crack growth between two dissimilar laminae. Using these fracture toughness measurements from the double cantilever beam specimens, some examples are given to show that the fracture criterion based on the mixed-mode stress intensity factors can accurately predict the failure load for various laminates under tensile loading conditions.