The pressure-induced phase transition in zinc sulfide is studied using a constant-pressure ab initio technique. The reversible phase transition from the zinc-blende structure to a rock-salt structure is successfully reproduced through the simulations. The transformation mechanism at the atomistic level is characterized and found to be due to a monoclinic modification of the simulation cell, similar to that obtained in SiC. This observation supports the universal transition state of high-pressure zinc-blende to rock-salt transition in semiconductor compounds. We also study the role of stress deviations on the transformation mechanism and find that the system follows the same transition pathway under nonhydrostatic compressions as well.