A modified pulse-phase ultrasonic technique for the measurement of the ultrasound velocity is described. It was applied for studies of the temperature dependence of the longitudinal ultrasound velocity in a nanocomposite MCM-41/LiCsSO₄in the temperature range 160-300 K. A local decrease of the velocity with minimum at ~195 K was observed. A qualitative explanation of this anomaly and its connection with the ferroelastic phase transition in the nanoparticles within the pores is given. It is shown that ultrasonic methods are very suitable for studies of the ferroelastic phase transitions in the nanocomposites.