We have investigated the electronic structure and magnetic properties of the full-Heusler alloy Co 2 MnSi (CMS) under external pressures and strains. The total and individual spin and orbital magnetic moments were also obtained under pressures and strains. We found a gradual transition from half-metallic to metallic state around 31 GPa in our relativistic study. The spin polarization degree (SPD) was reduced at the Fermi level by including relativistic effect of spin-orbit coupling. The exchange energy describes the trend of decreasing SPD values. The decreasing behavior observed for individual orbital magnetic moments under applied pressures. The metallic behavior was also observed under 8% strain along [001] direction. It was shown that the SPD values decrease in the presence of spin-orbit coupling, whereas the spin magnetism of Co 2 MnSi under uniaxial strain is marginally affected.