The work is devoted to the generalization of the difference method of spatial characteristics to the case of the plane problem of the propagation of waves in a rectangular region of finite dimensions with a symmetrically-located rectangular cutout at the lateral boundaries. Based on the numerical technique developed in this work, the calculated finite - difference relations of dynamic problems are obtained at the corner points of a rectangular cutout, where the smoothness of functions that is “familiar” to dynamic problems is violated. At these corner points, the first and second derivatives of the desired functions suffer a discontinuity of the first kind. The results of the study are brought to a numerical solution. The effect of stress concentration in the vicinity of the cutout was studied and it was shown that the impact of the cutout on the particle velocity distribution, on the stress distribution has a local character.