We study the shock-induced phase transformation from fullerite to a dense amorphous carbon phase by tight-binding molecular dynamics. For increasing hydrostatic pressures P, the C60 cages are found to polymerize at P<10 GPa, to break at P approximately 40 GPa, and to slowly collapse further at P>40 GPa. By contrast, in the presence of additional shear stresses, the cages are destroyed at much lower pressures (P<30 GPa). We explain this fact in terms of a continuum model, the snap-through instability of a spherical shell. Surprisingly, the relaxed high-density structures display no intermediate-range order.