Using the plane-wave pseudo-potential approach and generalized-gradient approximation for the exchange–correlation effects in the framework of the density functional theory, the structural, electronic, elastic and magnetic properties of X2CrSb ( ▪ and Cu) Heusler alloys were investigated. For ▪ , a structural phase-transition from XA to L21-phase is expected at 8.933GPa. This compound exhibits half-metallic behavior before becoming a magnetic metal at 17.5GPa. The ▪ is a half-metal under expansion and nearly half-metal above 1GPa. The total magnetic moments for ▪ , ▪ and ▪ are respectively equal to 5.0μB, 1.0μB and 3.4μB, and are mainly localized on Cr except for ▪ in XA-phase where the magnetic moment is localized on Mn. The DOS analysis shows weak spin-polarizations for ▪ and a higher polarization under expansion for ▪ and ▪ . Under compression, the polarization is weakened in ▪ , it remains at a high level before it vanishes at 29.4μB in ▪ .