Abstract
This work is devoted to the generalization of difference method of the spatial characteristics onto the case of the plane problem of wave propagation in a rectangular area of finite dimensions with breaks in the boundary conditions. On the basis of the developed in the work the numerical method it is obtained the calculated finite - difference ratio of the dynamic problem at the singular point of the lower border of the rectangular area, which is the point pairing of fixed and free parts of the boundary. The results of the study are brought to the numerical solution.