The charge density wave (CDW) nonlinear conductivity of the blue bronzes A(0.30)MoO(3) (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(0.30)MoO(3) single crystals in the temperature range 4-300 K. In Rb(0.30)MoO(3), at T∼50 K, upon cooling, a large increase of the sound velocity for the longitudinal mode measured along the [Formula: see text], [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(0.30)MoO(3). In V-doped samples, Rb(0.30)(Mo(1-x)V(x))O(3) (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.