The failure responses of adhesively bonded, hat stiffened structures are studied through numerical analysis using the finite element method. The responses are evaluated numerically for the bonded hat section/substrate structures containing different combinations of materials. It is studied what kind of material combinations causes the easier crack initiation in the structure. This study is conducted under plane strain conditions and J-integral via a commercial code ABAQUS as a total critical energy release criterion was used for observation on crack initiation. Also, the influence of adhesive on the structure is studied.