Diffraction of ultrasonic waves by immersed elastic bigratings constructed from the Galois fields GF(23) along one direction and GF(32) along the orthogonal one is studied. Such bigratings permit a significant attenuation of the specular echo in a wide frequency domain. This attenuation is experimentally observed and agrees with the theoretical one predicted by a model which takes into account the elasticity of the structure, the boundary conditions at the fluid–solid interface, and the periodicities of the gratings. Furthermore, numerous sharp minima in the spectrum of the reflection coefficient are experimentally observed and theoretically predicted; they correspond to the excitation of surface waves (generalized Rayleigh and Scholte–Stoneley waves) and they contribute significantly to the attenuation of the specular echo. ©1995 American Institute of Physics.