A complete contact problem of bonded condition is studied. Asymptotic analysis for a sharp notch problem is extended to incorporate the conditions of elastic dissimilarity and contact angle variation. Stress singularity at the contact corner is expressed by the generalized stress intensity factors (GSIFs) of mode I and II, with which a stress equation is described. Mode decoupling method is suggested to obtain the GSIFs. The characteristics of angular function in the stress equation are discussed. A simple example is solved to obtain the actual GSIFs with the assistance