Experimental studies and analysis of acousto-optic diffraction in $\alpha \text{-}{\mathrm{BaB}}_2{\mathrm{O}}_4$ and ${\mathrm{Li}}_2{\mathrm{B}}_4{\mathrm{O}}_7$ crystals are given. Ultrasonic wave velocity, elastic compliance and stiffness coefficients, and piezo-optic and photoelastic coefficients of $\alpha \text{-}{\mathrm{BaB}}_2{\mathrm{O}}_4$ and ${\mathrm{Li}}_2{\mathrm{B}}_4{\mathrm{O}}_7$ crystals are determined. The acousto-optic figure of merit has been estimated for different possible geometries of acousto-optic interaction. It is shown that the acousto-optic figures of merit for $\alpha \text{-}{\mathrm{BaB}}_2{\mathrm{O}}_4$ crystals reach the value $M_2=(270\pm 70)\times {10}^{-15}{\mathrm{s}}^3/\mathrm{kg}$ for the case of interaction with the slowest ultrasonic wave. The directions of propagation and polarization of those acoustic waves are obtained on the basis of construction of acoustic slowness surfaces. The acousto-optic diffraction is experimentally studied for $\alpha \text{-}{\mathrm{BaB}}_2{\mathrm{O}}_4$ and ${\mathrm{Li}}_2{\mathrm{B}}_4{\mathrm{O}}_7$ crystals.