We report on ultrasonic and elastic properties of acoustooptic (AO) Tl₃PSe₄ crystals. Acoustic wave (AW) velocities for different geometries are obtained experimentally, and complete matrices of elastic stiffness and compliance coefficients are computed. Anisotropy of AW propagation is analyzed. The minimal AW velocities are as follows: (i) 1902 m/s for the quasilongitudinal wave propagating at the angle 52 deg with respect to a axis in ab plane, (ii) 983 m/s for the quasitransverse wave QT1 propagating in cb plane along the bisector of b and c axes, and (iii) 526 m/s for the quasitransverse wave QT2 propagating along a (or b) axis. The geometries of AO interactions with the slowest acoustic eigenwaves are analyzed. Finally, AO figures of merit M₂ are roughly estimated for the cases of interactions with the slowest AWs. Within isotropic approximation for the elastooptic tensor they are equal to ∼ 1950 · 10^–15 s³/kg and ∼ 2800 · 10^–15 s³/kg at the isotropic interactions with the slowest quasilongitudinal wave and the slowest AW QT1, respectively. The M₂ parameter as high as ∼ 18800 · 10^–15 s³/kg can be expected for the case of anisotropic AO interaction with the slowest AW QT2.