Abstract <p>Pressure engineering has attracted growing interest in the understanding of structural changes and structure-property relations of layered materials. In order to obtain a better understanding of the phase stabilities and mechanical behaviors of Mn₃Sn compounds, the high-pressure compressibility, structural stability, and elastic properties of hexagonal Mn₃Sn have been investigated up to 30 GPa with density functional theory (DFT) calculations. The results show no evidence of structural phase transitions up to at least 30 GPa. The influences of pressure on lattice parameters, unit cell volume, and elastic constants are discussed. In addition, the polycrystalline elastic properties including bulk modulus, shear modulus, Young’s modulus, the ratio of shear to bulk modulus, and Poisson’s ratio are determined based on Voigt–Reuss–Hill approach. On the other hand, the metallic nature of this material was confirmed by density of states. We expect that our results will promote future experimental studies on Mn₃Sn.</p>