We report the first measurements of elastic modulus and energy dissipation in Ti-doped and undoped sodium aluminum hydride. It is shown that the chemical reactions that occur by varying the sample temperatures or by aging most sensitively affect the elastic constants, such that the modulus variations allow the time and temperature evolution of decomposition to be monitored. After a well-defined thermal treatment at 436 K, a thermally activated relaxation process appears at 70 K in the kilohertz range, denoting the existence of a new species, likely involving hydrogen, having a very high mobility, that is, 10(3) jumps/s at the peak temperature corresponding to a relaxation rate of about 10(11) s(-1) at room temperature. The activation energy of the process is 0.126 eV and the preexponential factor 7 x 10(-14) s, which is typical of point defect relaxation. The peak is very broad with respect to a single Debye process, indicating strong interaction or/and multiple jumping type of the mobile entity. The present data suggest that the models aiming at interpreting the decomposition reactions and kinetics should take into account the indicated point-defect dynamics and stoichiometry defects.