Acoustic studies of a nanocomposite consisted of MCM-41 molecular sieves with nanoparticles of ferroelastic LiCsSO<sub>4sub> within pores were carried out. The critical softening of the transverse ultrasound velocity was observed which evidenced the ferroelastic phase transition in confined particles. The transition was moved to low temperatures compared to that in bulk LiCsSO<sub>4sub>. It is shown that acoustic methods are very suitable to reveal the ferroelastic phase transitions under nanoconfinement.