We report sound velocity and ultrasonic attenuation measurements in the vicinity of the successive magnetic phase transitions Tmag1~6.5K, Tmag2~5.8K and Tmag3~5.3K in the charge density wave TbTe3 compound. A detailed investigation of the critical contributions to the temperature dependences of the sound velocity and ultrasonic attenuation is presented. Anisotropic stress dependences ∂Tmag1/∂σ found at the antiferromagnetic phase transition Tmag1 is associated with the layered structure of this compound. An abrupt step-like increase in the velocity and a sharp peak in the attenuation are observed with the longitudinal and shear modes at the lock-in magnetic phase transition Tmag3=5.3K. The critical velocity and attenuation behaviors in the high temperature paramagnetic above Tmag1 are described in terms of a phenomenological dynamic scaling expression. •Large anomalies in the velocity and ultrasonic attenuation at the magnetic phase transitions of TbTe3.•Critical behavior is analyzed.