The electronic structures and elastic properties of molybdenum disulfide are studied using first-principles calculations. The energy band structure and density of state (DOS) of MoS 2 at 0GPa are calculated. The band gap energy of MoS 2 versus the pressure 0–40GPa is obtained. We find that the band gap energy decreases as the pressure increases. The geometry optimized structural parameters for lithium nitride under different pressures are listed. The parameters a, c, and E (the enthalpy) all decrease with increasing pressure. However, parameter B (the bulk modulus), S (the shear modulus) and Y (the Young’s modulus) increase with pressure. The normalized lattice constants and the elastic modulus as two functions of pressure from 0–40GPa are obtained. All the calculated elastic constants C ij increase by different rates with increasing pressure.