  The behavior of $\alpha$-quartz under hydrostatic and non-hydrostatic
high-pressure conditions has been investigated in Molecular Dynamics
simulations of silica in order to clarify the role of non-hydrostatic stresses
in the amorphization process. It is shown that the amorphization threshold is
not modified if the stress along the {\bf c} direction is lowered, so that the
mean amorphization pressure can effectively be lowered under non-hydrostatic
conditions. On the other hand, the application of a positive uniaxial stress
along the {\bf c} axis, results in the appearance of a new crystalline phase,
where all silicon atoms are in five-fold coordination.
