An ultrasonic pulse–echo method was used to measure the transit time of longitudinal (10 MHz) and transverse (5 MHz) elastic waves in a polycrystalline sample of the L12 Al5CrTi2 intermetallic compound. The measurements were carried out under hydrostatic pressure up to 1 GPa at room temperature. On the basis of experimental data the velocities of longitudinal and transverse ultrasonic waves, density, elastic moduli and Debye temperature of the material were calculated as a function of pressure. The parameters of the isothermal Murnaghan’s equation of state were obtained (isothermal bulk modulus, BT0=115 GPa, and its pressure derivative, (dBT/dp)0=5.4, at ambient conditions). The value of the shear modulus of this intermetallic at ambient conditions, G0=75 GPa, was found to be nearly three times as high as that for aluminium, which is the main component (62.5 at.%) of the alloy. The shear modulus of Al5CrTi2 increases under pressure faster ((dG/dp)0=2.34) than that of most simple metals. A pressure of 1 GPa increases Poisson’s ratio (0.237) only by ∼1.3%. These results confirm qualitatively the theoretical predictions concerning the features of interatomic bonding in the L12 lattice of this alloy.