The elastic, electronic, and structural features of the binary compounds HoX₃ (X = Pd, Pt) are theoretically studied using density functional theory. The implications of include the exchange-correlation potential is investigated using a generalized gradient approximation with an extra Hubbard-U component to account for the Coulomb on-site interaction (GGA+U). Elastic constants of these compounds are calculated, and their properties are examined. In addition, additional essential factors such as the Poisson's ratio, Young moduli, Shear moduli, Bulk moduli, and Cauchy pressure are studied. These compounds are both ductile and mechanically stable. Their band structures and state occupancy in spin-up and spin-down modes show the metallic character of these compounds.