We present results on the bonding nature, structural, electronic, magnetic and elastic properties of $\rm{REIr}_{3}$ ($\rm{RE = Gd, Tb}$ and $\rm{Ho}$) intermetallic compounds adopting simple cubic $\rm{AuCu_{3}}$-type structure obtained using the full-potential linearlised augmented plane wave (FP-LAPW) method based on density functional theory. The local spin density approximation (LSDA) with Hubbard parameter ($\rm{LSDA} +U$) has been used for exchange and correlation effects to get accurate results because of the presence of highly localised $4 f$ electrons of rare-earth $\rm{(RE) (RE = Gd, Tb}$ and $\rm{Ho}$) atoms. The calculated lattice parameter is found to be consistent with the experimental results. The calculated magnetic moments predict ferromagnetic behaviour of these compounds. The electronic and bonding properties have been solved in terms of band structure, density of states (DOS) and charge density plots. These results confirm the metallic nature of these compounds. The bonding appearances of these compounds have also been interpreted from charge density plots. The elastic constants, shear modulus and Cauchy’s pressure are computed and they reveal that $\rm{GdIr_{3}}$ and $\rm{TbIr_{3}}$ compounds are ductile while $\rm{HoIr_{3}}$ shows brittle character.