Аннотация:This report deals with the behaviour of electromagnetic field in the vicinity of the edge of a waveguide’s boundary or near the edge of the surface of discontinuity of permittivity inside a waveguide. With the use of the method, first introduced in the works of V.A. Kondratiev, the solution is represented as a sum of the singular part of the field, whose form is found explicitly, and the smooth additive, which is evaluated through the norm of a corresponding functional space.