We present high-resolution surface Brillouin scattering measurements on cubic GaN layers grown on GaAs substrate. By using a suitable scattering geometry, scattering by surface acoustic waves is recorded for different azimuthal angles, and the surface acoustic wave velocities are determined. A comparison of experimental results with numerical simulations of the azimuthal dependence of the surface wave velocity shows good agreement and allows a consistent set of elastic constants for c-GaN to be determined. © 2016 The Japan Society of Applied Physics. ; This work was partially supported by the Spanish MINECO under projects MAT2012-37276-C03-01 and MAT2015-71035-R, and from Comunidad de Madrid project S2013=MIT-2740 (PHAMA_2.0-CM). One of the authors (C. Kopittke) acknowledges the DAAD and its RISE program for financial support. ; Peer reviewed