We have studied experimentally the acoustic wave velocities for TlInS2 crystals and determined all components of their elastic stiffness and compliance tensors. It has been found that TlInS2 reveals small elastic anisotropy with respect to normal mechanical stresses. The compliance components S44 and S55 are very large, thus suggesting that the TlInS2 crystals are extremely compliant to the shear stresses in the cleavage plane. We have also revealed that the velocities of some of the quasi-transverse waves are very low (∼725 m/s), leading to extremely high acousto-optic figures of merit (∼2200-9000×10-15 s3/kg). This implies that the crystals under study can prove to be a very efficient acousto-optic material.