Wepresent a comparative study of the anisotropy in the elastic properties of the C49,C54 and C40 phases of TiSi2, as well as orthorhombic TiSi and hexagonal Ti5Si3. The elastic constants, elastic moduli, Debye temperature and sound velocities are computed within the framework of density functional theory. The computed values of the elastic constants and moduli are found to be in excellent agreement with available experimental values. The average elastic moduli, such as Young's modulus, shear modulus, bulk modulus and Poisson's ratio, of polycrystalline aggregates are computed using the computed elastic constants of single crystals. The anisotropy in elastic properties is analyzed using estimates of shear anisotropic factors, bulk modulus anisotropic factors and variations in Young's and bulk moduli in different crystallographic directions. Among the Ti-Si phases, the computed directional Young's modulus profiles of C49 TiSi2 and C40 TiSi2 are found to be quite similar to those of bulk Si and Ti, respectively. In addition to the elastic properties, the electronic structure of five Ti-Si phases is studied. The density of states and planar charge density profiles reveal mixed covalent-metallic bonding in all Ti-Si phases. © 2015 IOP Publishing Ltd.