This study analyzes the lattice dynamics of HgS under various pressures using ab initio self-consistent calculations based on the plane-wave method (PW) and generalized gradient approximation (GGA). The static study, performed by enthalpy calculations, predicts that the transition from the cinnabar phase (α-HgS) to the zinc-blende B$_3$ (β-HgS) or wurtzite (2H) structures occurs at very low pressures, at 0.65 or 0.70 GPa, respectively. Furthermore, the transition from β-HgS to the rocksalt (B$_1$) phase occurs at 7 GPa, and at high pressure, specifically at 110 GPa, HgS can adopt the CsCl (B$_2$ ) phase. The mechanical study confirms the stability of the β and 2H phases at 0 GPa. Phonon calculations corroborate the results of the static and mechanical studies regarding stability α$^{0.7GPa}$→ 2H $^{0.9GPa}$→ β , and the results indicate that the instabilities of the transverse acoustic (TA) modes, induced by the application of pressures of 10.5 GPa, 21 GPa, and 190 GPa, are responsible for the observed phase transitions in part of the Brillouin.