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