To shed further light on the dynamics of the martensitic transformation in shape-memory alloys, measurements have been made of the effects of hydrostatic pressure on the velocities of 15 different pure ultrasonic modes propagated at room temperature in a single-crystal alloy in its 18R martensitic phase. Although the point symmetry group of the 18R martensite is monoclinic, the elastic behaviour can be reasonably described in terms of an orthorhombic structure; the further monoclinicity beyond such an orthorhombic representation is very small and can be neglected to a first approximation. The results obtained for the nine independent second-order elastic stiffness tensor components in the 18R structure and their hydrostatic-pressure derivatives have been used to calculate the mode Grüneisen parameters , which quantify the vibrational anharmonicity of long-wavelength acoustic phonons. Results are compared with those computed from TOEC data measured on a -phase Cu-Zn-Al single crystal with a similar composition. At room temperature, about 28 K below the martensitic transition temperature (= 323 K), the longitudinal mode have normal, positive values; however, those associated with some shear modes have negative values. A pronounced minimum has been found in the Grüneisen parameter of the shear mode propagated along the [111] direction with polarization vector. It is concluded that the lattice stability against this particular shear mode decreases as the sample approaches the martensitic transition.