The problem of determining the stress field in an elastic space containing a defect with a cross-section in the form of a broken line is solved. Cases of a crack or a thin rigid inclusion are considered. It is assumed that the defect is under the action of a harmonic wave of longitudinal shear. The solution method consists in the fact that the displacement of the reflected wave is represented as a sum of discontinuous solutions of the Helmholtz equations, constructed for each link of the defect. As a result, in the case of a crack, the original boundary value problem is reduced to a system of singular integro-differential equations of unknown jumps in displacements on its links. f the defect is a thin rigid inclusion the original problem is reduced to a system of singular integral equations to stress jumps on its links. A feature of the obtained systems is that the singular components of the kernels of the integral equations contain immobile singularities. The presence of immobile singularities strongly affects the asymptotics of solutions of singular integral equations. These asymptotics was analyzed and considered in the determination of the class of functions in which we construct approximate solutions. For numerical solving the obtained. Systems of equations the method that takes into account the true asymptotics of unknown functions and uses special quadrature formulas for singular integrals is created.