We report on the results of a large-scale molecular dynamics simulation study of shock-wave propagation in pristine amorphous silicon carbide and carbon-nanotube-reinforced amorphous silicon carbide matrix composites. We seek to understand the effects of ensembles of aligned nanotubes, both transversely and longitudinally oriented, on the shock-wave structure and dynamics and structural rearrangements taking place in the shock-loaded composite materials. It is found that the presence of aligned nanotubes in amorphous silicon carbide matrix leads to a reduction of shock-wave velocity and modifies the shock-wave front structure in a wide range of impact velocities. The temporal evolution of density profiles behind the shock-wave front is studied and conclusions are drawn regarding the effects of carbon nanotubes on the structural rearrangements in the shock-loaded composite materials. The mechanisms of carbon nanotube failure under shock loadings and their implications for energy dissipation rates in composite material systems are discussed for both considered cases of carbon nanotube alignments.