The two-dimensional problem of the plane wave scattering by a periodic grating, an echelette with a right angle, is considered in the case of high-frequency approximation (the wavelength is assumed to be small compared with the period of grating) and where only one face of a wedge is illuminated. The ray optical solution to the problem (short-wave asymptotic result) derived on the basis of the method of summation of multiple diffracted fields, which is well-known in the geometric theory of diffraction, is described. Numerical results are presented and compared with calculations based on an integral equation approach. ¿ American Geophysical Union 1996