Structural, electronic, elastic, optical, and vibrational properties of ternary half-Heusler compounds HfXSb (X = Co, Rh, Ru) were studied with means of ab initio calculations based on the density functional theory. The calculated lattice constants were in good agreement with the available data. The electronic structure and corresponding density of states (DOS) were also calculated. Indirect band gaps were observed for HfCoSb and HfRhSb. Due to some valence bands crossing the Fermi level, HfRuSb has metallic character. In addition to the electronic structure, elastic and optical properties, phonon dispersion curves and phonon DOS were calculated. A detailed comparison was made between these three half-Heusler compounds.