Abstract. We have experimentally studied the acoustic and elastic anisotropies of AgGaGeS 4 crystals. Basing on the acoustic wave velocities measured, we have determined the complete matrices of elastic stiffnesses and compliances. We have found that the orthorhombic unit cell of AgGaGeS 4 is only slightly distorted with respect to the prototypical tetragonal lattice. We have revealed a quite rare effect in AgGaGeS 4 crystals, an equality of the velocities of quasi-transverse and quasilongitudinal waves. When propagating along the direction of a so-called longitudinal-transverse 'acoustic axis', these waves become 'half-transverse' and 'half-longitudinal'. It has been found that the quasi-transverse acoustic wave that propagates in the crystallographic plane ac with the velocity 1570 m/s is the slowest wave in AgGaGeS 4 . The acoustooptic figure of merit for our crystals calculated following from the velocity of the slowest acoustic wave and rough estimation of the elastooptic coefficient can reach 500 . This suggests that AgGaGeS 4 can be a promising material for acoustooptic applications in the mid-IR spectral range.