The structural, elastic, elastic anisotropy and electronic properties of ferroelectric SbSI and paraelectric SbSI, SbSeI and SbTeI crystals were computed using the local density approximation with first-principle calculations, based on density functional theory. The independent elastic constants of SbXI compounds were computed and the results reveal that they are mechanically stable. Some polycrystalline quantities such as bulk modulus, shear modulus, acoustic velocities, Young's modulus, Poisson's ratio, elastic anisotropy and elastic Debye temperatures of these compounds were derived from computed elastic constants. Energy band structures show that these compounds have an indirect band gap. The electronic charge distribution and partial density of states of SbXI compounds indicate that the Sb-X bond is typically covalent with a strong hybridization as well as Sb-I compounds that have strong ionic character. The results obtained were compared with experimentally measured values and other theoretical data.