<p>The problem of wedging an elastic wedge by a rigid plate of constant thickness along a semi-infinite crack on its axis of symmetry is considered. At infinity, each of the half-wedges is not loaded and rotates from the axis of symmetry of the wedge by a certain angle. Friction forces in the contact domain of each of the crack faces with the plate are not taken into account. An integral equation of the problem with a difference kernel on a system of finite and semi-infinite intervals is obtained. Using the Wiener–Hopf method, the integral equation is reduced to an infinite system of algebraic equations with exponentially decreasing coefficients, which is solved by the reduction method. The size of the contact domains and the angle of rotation of the half-wedges at infinity are determined. The stress distributions in the contact domains and on the crack extension, the normal displacements of the crack faces, the stress intensity factor, and the contact stress intensity factor are obtained. It is shown that taking into account rotation at infinity significantly reduces the intensity of stresses in the vicinity of the crack tip and at the edges of the contact domains of the crack faces with the plate.</p>