The set of elastic constants of the charge density wave (CDW) rare earth tritelluride TbTe3 has been measured at 15MHz in the temperature range 300–360K. Large anomalies in the velocity and ultrasonic attenuation of the longitudinal C11 and C33 modes are observed at the charge density wave phase transition TCDW=333K. Anisotropic stress dependence ∂TCDW/∂σ is found, the components ∂TCDW/∂σ11 and ∂TCDW/∂σ33 in the (a,c) plane are one order of magnitude larger than the component ∂TCDW/∂σ22 perpendicular to it. The Landau theory has been used to explain the experimental data. Critical behaviour near the charge density wave phase transition is described in terms of a phenomenological dynamic scaling theory. •Set of elastic constants of rare earth tritelluride TbTe3 crystals are reported.•Large anomalies in the velocity and ultrasonic attenuation at the charge density wave phase transition.•Critical behaviour is analyzed.