This paper describes the application of Impulse Stimulated Thermal Scattering (ISTS) for measurement of surface acoustic wave (SAW) velocity and thermal diffusion along a free surface of a strongly anisotropic material. The motivation for this work stems from the study of thermoelastic properties of individual phases of ferroelastics; experimental results were obtained on a single crystal in the austenitic phase a Cu-Al-Ni alloy (bcc single crystal having elastic anisotropy factor of about 12). The measured SAW velocities in specific directions are in a good agreement with the values calculated for the elastic constants obtained by other ultrasonic methods. Similarly, the evaluated thermal diffusivity coefficient (22 ± 2).10−6 m2/s of the austenite is consistent with the data in the literature. The proposed approach has also a potential for characterization of thin films grown on anisotropic substrates.