A piecewise-homogeneous elastic orthotropic plate, reinforced with a finite patch of the wedge-shaped, which meets the
interface at a right angle and is loaded with tangential and normal forces is considered. Using methods of the theory of
analytic functions, the problem is reduced to the system of singular integro-differential equations (SIDE) with fixed singularity.
Under tension-compression of patch using an integral transformation a Riemann problem is obtained, the solution
of which is presented in explicit form. The tangential contact stresses along the contact line are determined and their
asymptotic behavior in the neighborhood of singular points is established.
