A method is described for modelling 3D elastic data in anisotropic media, based on the pseudospectral approach. The goal is to model the effects of azimuthal anisotropy on 3D shear-wave data, in particular the phenomenon of shear-wave splitting. The pseudospectral approach is used in preference to other gridded methods on efficiency grounds, because of its economy in the number of grid points required. Numerical issues, including dispersion, boundary effects and non-local operator artifacts are discussed, and solutions to them are provided. A comparison with the analytic result for a displacement source in a homogeneous medium shows the high accuracy of elastic pseudospectral modelling. Preliminary results of modelling in 2D and 3D anisotropic models are presented and analyzed. The expected shear-wave behaviour is observed in simple cases. This pseudospectral modelling technique is suitable for testing multicomponent processing or imaging algorithms in the presence of anisotropy.