We present specific heat and ultrasonic measurements on the rare earth tritelluride ErTe3 compound. Thermodynamic anomalies are observed at the upper charge density wave (CDW) phase transition TCDW1=265K and the second one at TCDW2=155K. Similar critical behaviors are found at both CDW phase transitions and that we tentatively described in terms of the 3D XY model. Different anisotropic stress dependences ∂TCDW1/∂σii and ∂TCDW2/∂σii are found at the two successive CDW phase transitions. Magnitude of the elastic constant anomalies at TCDW2 is ten times smaller than that at TCDW1. Anomalies in the elastic constants at the upper CDW TCDW1 exhibit two dimensional features in the layer planes while in contrast a three dimensional behavior is observed at TCDW2.