  Close to the Mott transition, lattice degrees of freedom react to the
softening of electron degrees of freedom. This results in a change of lattice
spacing, a diverging compressibility and a critical anomaly of the sound
velocity. These effects are investigated within a simple model, in the
framework of dynamical mean-field theory. The results compare favorably to
recent experiments on the layered organic \kappa-(BEDT-TTF)_2Cu[N(CN)_2]Cl
conductor . We predict that effects of a similar magnitude are expected for
V2O3, despite the much larger value of the elastic modulus of this material.
