We use hybrid density functional theory, including van der Waals interactions, to study the elastic properties of bulk molybdenum disulfide (MoS 2 ). We determine a complete, consistent set of accurate values for elastic constants, overcoming the inconsistencies in the reported values in the literature. We also elucidate the changes in materials properties that occur when hydrostatic pressure is applied. The compression ratio, the transition from semiconductor to semimetal, and the pressure dependence of the elastic constants are discussed. The good agreement with experiments for small hydrostatic pressures validates our methodology and our calculated values for the elastic constants.