The structural and elastic properties of the ternary silicides ScTSi (T═Co, Ni, Cu, Ru, Rh, Pd, Ir, Pt) and of the equiatomic intermetallic YTX (T═Ni, Ir; X═Si, Ge, Sn, Pb) are studied using the density-functional theory considering the orthorhombic TiNiSi crystal structure with space group Pnma. From the calculated formation energy, we obtained the following stability order of: ScCuSi < ScCoSi < ScRuSi < ScNiSi < ScPdSi < ScRhSi < ScIrSi < ScPtSi and YNiPb < YNiSn < YNiGe < YNiSi < YIrSn < YIrGe < YIrPb < YIrSi. The lattice parameters and atomic positions are in good agreement with experiments to $1%. All the alloys are mechanically stable using the Born elastic stability criteria. Ductile behavior inferred from the Pugh ratio, shear over bulk modulus G/B, and the Cauchy pressure, could be observed only for ScTSi (TÀ À À ÀRu, Pd, Pt) and YNiSn compounds and moderately for YIrX (Si, Ge, and Sn) and YNiPb. On the contrary, ScTSi (TÀ À À ÀCo, Ni, Cu, Rh, Ir), YNiGe, and YNiSi compounds are covalent or exhibit G/B > 0.5, leading to a brittle behavior in accordance with the Poisson ratio value. The Zener anisotropy factor is different from 1, indicating that these compounds are elastically anisotropic materials. A strong correlation is found between G and the Young's modulus E, slightly above G $(3/8)E widely found for polycrystalline metals.Correlation trend between the Young's modulus E and the shear modulus G of intermetallic compounds.1 Introduction The ternary compounds: scandium (IIIB group element) and 3d/4d/5d transition-metal silicides, i.e., ScTSi (T═Co, Ni, Cu (3d), Ru, Rh, Pd (4d), Ir, Pt (5d) from VIIIB group) and the equiatomic tetrelides YTX (Y being the yttrium, T═Ni, Ir; X═Si, Ge, Sn, Pb from IVA group) crystallize in the orthorhombic TiNiSi-type crystal structure (space group Pnma, Z ¼ 4) [1][2][3][4][5][6][7][8][9][10][11][12]. The incorporation of the transition metals and of p-block elements such as Si [13] modifies the magnetic interactions between the rare-earth atoms in ScTSi compounds leading to a large variability of their interesting physical properties such as magnetocaloric effects and magnetoresistance. In the field of magnetic materials research, rare-earthtransition-metal intermetallic compounds have always