Failure in anisotropic/isotropic bi-materials starts at the interface, and the interfacial failure is of interest to some engineering fields such as automobile and aviation industry. Many researchers have done a lot of research on this field, but many did not consider a specific stress component near the interface corner tip as a parameter of a failure criterion. Kun Cheol Shin, introducted a failure criterion for anisotropic/isotropic bi-materials problem with a wedge. But the process of obtaining the singular stress fields of anisotropic/isotropic bi-materials is complex. To solve this problem, we have taken a new method which is from Xuecheng-Ping and M.-C. Chen.The method is new, which is based on displacement and more easily in calculating the stress and displacement fields surrounding a wedge tip than before. Through this method, we establish a criterion base on the-plan. The failure criterion can be used not only to predict stress intensities of co-cured double lap joints that with thermal and mechanical load, but also to predict stress intensities of co-cured double lap joints that with different materials or lap length. And we describe the process of calculating singular stress fields and stress intensities of co-cured double lap joints with a wedge that consists of glass fiber reinforced composites and steel adherends.