A bi-material problem is analyzed for bonded dissimilar two half-planes using a rational mapping function and complex stress functions. The half-planes are bonded in the finite length with cracks and subjected to coupling force and external force applied at infinity. The cracks have the same length at an end of the interface and perpendicular to the interface in each material. This analytical model can be used for the investigation of the crack initiation from the interface debonding tip. The stress analysis is carried out and the stress distribution and stress intensity factors are obtained. By focusing on an interface debonding tip, it is possible to decide analytically the fracture phenomena. The conditions of occurrence of debonding extension and crack branching are examined under different coupling and external forces for various material constants.