In the lithium-caesium sulphate crystal in the temperature range of ferroelastic phase transition, the uniaxial stress σ
X induced changes in velocity and attenuation of the longitudinal ultrasonic wave propagating in the direction  are studied. The phase transition is close to the three-critical point and the critical exponent is κ = 0.27 ± 0.02. The stress applied drastically decreases the stepwise change in the wave velocity at T
C up to its disappearance at 2 MPa. In the temperature range between T
C and T
C − 6 K, the stress leads to an increase in the wave velocity and a decrease in its attenuation. This range was interpreted as that of co-existence of ferroelastic and incommensurate ordering, in which the stress influences the density of solitons leading to stiffening of the crystal lattice.