The problem of two semi-infinite elastic planes with different elastic properties bonded to each other along a finite number of straight-line segments and subjected to loads at infinity is formulated and the solution of the problem is reduced to the evaluation of ordinary integrals. The solutions for the cases with one and two bonding segments are given. For the general case, the stress state near the crack tips is analyzed and it is shown that the stress singularity is in the form of r−1/2, r being the distance from the crack tip. Finally, the stress-intensity factors, which are used in the fracture mechanics and which can be taken as the measure of the strength of stress singularities, are expressed in terms of the complex stress function.