<p>We consider the equilibrium of two rigidly connected elastic half planes made of different materials and containing a semi-infinite thin rigid inclusion on the interface of material. One side of the inclusion is connected to one of the half planes. The other side is exfoliated with formation of a crack. Normal and tangential concentrated forces are applied to one of the crack edges. The frictional contact of the crack edges near its tip is taken into account. By using the Wiener–Hopf method, the solution of the integral equation of the problem is obtained in the closed form. We determine the size of the contact zone of the crack edges and the distributions of stresses in the contact zone, on the interface between the half planes outside the crack, and in the zone of connection of the inclusion with the half plane.</p>