The structural and mechanical properties of ZnS in both B3 and B1 phases have been investigated by the generalized gradient approximation (GGA) within the plane-wave pseudopotential density functional theory (DFT). The obtained lattice parameters and bulk modulus of ZnS for both B3 and B1 structures are well in line with the available theoretical and experimental results. Using the enthalpy–pressure data, we have predicted that the phase transition pressure of ZnS from B3 to B1 is 17.26 GPa, which is in good agreement with previous experimental values. The hydrostatic pressure-dependent elastic properties of the two structures, such as bulk modulus, shear modulus and Young’s modulus, are discussed. Then, the mechanical characteristics of ZnS, including ductile/brittle behavior and elastic anisotropy of the two cubic single-crystal structures, are investigated in details. Furthermore, the thermodynamic properties of ZnS under extreme condition are explored by quasi-harmonic Debye modeling. The calculated results show that the ductility and elastic anisotropy increase with pressure clearly except the ductility of B1. Besides, the temperature and pressure dependencies of the heat capacity and the Debye temperature are obtained and analyzed in the wide ranges.