[en] The charge density wave (CDW) nonlinear conductivity of the blue bronzes A_0.30MoO₃ (A = K, Rb) shows two different regimes depending on the temperature: a strongly damped CDW motion above ∼50 K and a CDW motion with almost no damping below ∼50 K. In a search for an elastic signature of this CDW behaviour, we performed ultrasonic measurements on A_0.30MoO₃ single crystals in the temperature range 4-300 K. In Rb_0.30MoO₃, at T∼50 K, upon cooling, a large increase of the sound velocity for the longitudinal mode measured along the 2-bar01, [102] and b directions is observed. The ultrasonic attenuation coefficient shows an increase down to 50 K followed by a plateau. Similar results are found in K_0.30MoO₃. In V-doped samples, Rb_0.30(Mo_1-xV_x)O₃ (x = 0.4%) the anomaly broadens and is shifted towards higher temperatures. The results are discussed in relation to the changes in the CDW rigidity, disorder and dielectric response. A scenario based on a glass transition for the CDW superstructure is proposed.