We have developed a multidomain pseudo-spectral method for 3-D anisotropic seismic waveform modelling to run in a high-performance parallel computer. The numerical scheme solves acoustic and elastic wave equations formulated by velocity and stress for fluid layers and solid spaces, respectively. Spatial variations of velocity and stress fields propagating in general anisotropic and heterogeneous media are calculated by high-accuracy Fourier and Chebyshev differential operators. The fourth-order Runge–Kutta method is employed for time-marching of the wavefields. The domain decomposition technique divides the full space into several subdomains bounded by discontinuous features with steep velocity gradients. The propagating wavefronts are separately calculated in each subdomain, then wavefield matching procedures subject to the continuity condition for the velocity and traction are imposed at the interface of subdomains. Non-periodic boundary conditions at the free surface and the non-reflected edge at the bottom of the model space are adequately represented by expansion in Chebyshev polynomials. Parallelizing the serial algorithm effectively reduces the computation time. Data locally distributed in many processors for the parallel program provides the large memory storage needed for a 3-D model. The waveforms calculated by this numerical scheme show accuracy comparable with a known analytical solution. The numerical experiments indicate the effectiveness of the multidomain approach in modelling seismic energy partitioning into reflected, refracted and transmitted waves at velocity discontinuities such as the crust/water interface and in generating synthetic seismograms at seafloor affected by water reverberations. We simulate seismic wave propagation in isotropic and anisotropic elastic media with hexagonal, orthorhombic and monoclinic symmetries, which represent possible symmetry systems in the mantle and crust. The propagating wavefields possess observable differences in wavefront geometry, phase arrivals, disturbed amplitude and shear-wave splitting. The azimuthal dependence in traveltimes and variability in synthetic waveforms demonstrates that fine details of anisotropic velocity structures can be resolved by comparing simulated full waveforms with observed seismograms recorded at various distances and azimuths.