A significant attenuation of the specular echo in a wide frequency domain occurs in scattering of waves by Galois gratings. Diffraction of ultrasonic waves by immersed one‐dimensional elastic gratings constructed from the finite Galois fieldsGF(pm) is investigated. We develop a theoretical model taking into account the elasticity of the structure, its finite thickness, the boundary conditions at the fluid–solid and solid–fluid interfaces, and the periodicity of the gratings. In addition to the typical attenuation of the specular echo predicted by discrete Fourier transform, such a model predicts minima in the spectrum of the reflection coefficient corresponding to the excitation of surface waves (generalized Rayleigh and Scholte–Stoneley waves) by mode conversion and to the excitation of Lamb‐type modes. The attenuation as well as the minima are experimentally observed and these results are in good agreement with theoretically predicted ones. Galois gratings could constitute an advance in the search for new anechoic devices. ©1996 American Institute of Physics.