The structural, elastic and electronic properties of XCoSb along with the impact of pressure on the structure of the compounds are discussed in this paper. Calculations have been carried out using the pseudopotential plane wave method within generalized gradient approximation according to the Perdew-Burke-Ernzerhof (GGA-PBE) method. At ambient conditions, XCoSb crystallizes in a C1b-type cubic structure and we observed that at high-pressure VCoSb, CrCoSb and MnCoSb undergo a phase transition from cubic to the LiGaGe-type hexagonal structure. Elastic constants are reported for the first time. The electronic band structure and density of states (DOS) show that ScCoSb and TiCoSb are semiconductors and non-magnetic while VCoSb, CrCoSb and MnCoSb are half-metallic ferromagnetic. In addition, we have also calculated elastic moduli, Zener anisotropic factor, Poisson’s ratio and transverse and longitudinal sound velocities from the second-order elastic constant.