Magnesium and its compounds are recognized as favorable materials for structural uses, primarily due to their lightweight nature and remarkable specific strength. This research employed first-principles methodologies to investigate how pressure affects the crystal structure along with the elastic and thermodynamic characteristics of MgXY₂ (X=Zn, Cd, and Y= Ag, Au, Cu) compounds. All analyses were implemented via the Perdew-Burke-Ernzerhof variant of the Generalized Gradient Approximation alongside a plane-wave ultrasoft pseudopotential approach. The findings on the elastic constants indicated that these MgXY₂ compounds have maintained their stability at pressures up to 500 kBar. These constants informed detailed assessments of properties like elastic modulus, Poisson’s ratio, Vickers hardness, and material anisotropy. The Quantum Espresso software was utilized to calculate melting points, Debye temperature, and minimum thermal conductivity values. A temperature range spanning from 0 to 800 K allowed for an evaluation of vibrational energy, free energy, entropy, and specific heat capacity metrics. The anticipated physical attributes suggest significant potential for these magnesium compounds in biomedical fields.