First-principles calculations of elastic and thermodynamic properties of CaS in NaCl structure under high pressures are conducted by using plane-wave pseudopotential density functional theory method and quasi-harmonic Debye model. Calculated lattice constants and elastic modulus at P=0 GPa and T=0 K are in good agreement with experimental data. It shows that influence of pressure on elastic modulus and thermal expansion coefficient is greater than that of temperature. Heat capacity decreases with increase of pressure under same temperature and tends to Dulong-Petit limit at high temperatures. By solving Gibbs free energy, phase transition pressure between B1 structure and B2 structure of CaS is obtained at 36.61 GPa.