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In this computational study, density functional theory (DFT) is employed to analyze the structural, electronic, elastic, and topological properties of ternary compounds MXY (M = Ti, Sn, Ir, X = Se, Te, Y = Se, Te). The effects of spin–orbit interaction and pressure‐induced strain are investigated to understand their influence on the stability, mechanical properties, and electronic behavior, paving the way for potential technological applications. The findings confirm that these compounds are inherently stable in nonmagnetic phases, with spin–orbit interaction critically influencing their energy–volume landscapes. The calculated lattice parameters, ratios of lattice constants, and bulk moduli closely align with existing data, confirming the reliability of our approach. Mechanical assessments reveal distinct behaviors: IrSe₂exhibits the highest stiffness due to pronounced covalent bonding, contrasting with SnTe₂'s elastic anisotropy and SnSeTe's nearly isotropic properties. Electronically, most compounds show metallic characteristics, except SnSe₂, which behaves as a semiconductor with an indirect, pressure‐sensitive energy bandgap. Topological analysis under varying hydrostatic pressures indicates band inversions in TiSe₂, IrSe₂, and SnSeTe, suggesting topological phase transitions absent in other compounds. This study enriches our understanding of these materials and refines the application of DFT in material design.