First-principles calculations of the crystal structures, phase transition, and elastic properties of B1-B2 phase calcium sulfide (CaS) have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values (for crystal structures and the phase transition) are in very good agreement with experimental data as well as with some of the existing model calculations. The dependence of the elastic constants c(ij), the aggregate elastic modulus, the deviation from the Cauchy relation, and the elastic anisotropy on pressure have been investigated. The normalized elastic constants c(ij)' have been introduced to investigate the elasticity of CaS in detail. Moreover, the variation of the Poisson ratio, Debye temperature, and longitudinal and transverse elastic wave velocity with pressure P up to 70 GPa at 0 K have been investigated for the first time.