Discrete element modelling (DEM) of a face-centred cubic assembly of spherical particles has been used to study the influence of anisotropic stress states on the shear wave velocity of a granular material. The shear waves were generated and detected in a way equivalent to the use of bender elements in laboratory testing. Comparisons are presented between the discrete element simulations and analytical and empirically derived methods of relating stiffness to the degree of confining stress anisotropy. The results confirm previous empirical observations that wave velocity is strongly influenced by the stresses in the direction of propagation and in the direction of oscillation of the shear wave. The wave velocity is, however, largely independent of the stress orthogonal to the plane containing the wave motion.