The resistance to crack growth exhibited by a quasi-isotropic double cracked-lap-shear specimen made of AS4/3502 graphite/epoxy materials was investigated. The factors reported earlier to influence delamination behavior such as fiber bridging, fiber breakage, and curing stresses were examined to assess their effect in the specimen. It was found that the prevalent damage modes for this specimen design were matrix microcracks and delamination. These two modes interact to produce the resistance behavior observed under tensile loading. The quantitative assessment of resistance was based on an engineering intuitive approach. Matrix microcracking was induced by the strain concentration at the crack front. Delamination onset was determined using a fracture mechanics approach based on the total energy release rate and the energy release rate components. When compared with test results, the predictions of the analytical model provide a rational physical explanation of the resistance behavior.