The structural, electronic, and elastic properties of hexagonal layered crystal MoS 2 under pressure are investigated using first-principles calculations within the local density approximation (LDA). The calculated lattice parameters a 0 , c 0 , and cell volume V 0 of MoS 2 are in good agreement with the available experimental data. Our calculations show that MoS 2 is an indirect band gap semiconductor and there is a vanishing anisotropy in the rate of structural change at around 25 GPa, which is consistent with the experimental result. We also analyse the partial density of states (PDOS) of MoS 2 at 0 and 14 GPa, which indicate that the whole valence bands of MoS 2 are mainly composed by the Mo-4 d and S-3 s states at 0 GPa, while they are mainly composed by the Mo-4 p , Mo-4 d , and S-3 p states at 14 GPa. The electronic charge density difference maps show the covalent characteristic of Mo–S, and the bonding properties of MoS 2 are investigated by using the Mulliken overlap population. In addition, the elastic constants C ij , bulk modulus B , shear modulus G , Young’s modulus Y , the Debye temperature Θ D , and hardness H of MoS 2 are also obtained successfully. It is found that they all increase monotonically with the increasing pressure.