Abstract First principles calculations of anisotropic elastic constants of titanium boride (TiB) have been performed using the computational implementation of density functional theory (DFT). TiB has orthorhombic crystal structure, thus, nine independent elastic constants need to be determined to completely characterize its polycrystalline elastic behavior as well as elastic anisotropy. TiB, especially in the whisker form, has attracted attention recently as reinforcement in metal matrix composites, wear resistance coatings and has potential as monolithic material due to its high hardness and elastic modulus coupled with its electrically conducting nature. In this study, the elastic constants were determined using the WIEN2K computational implementation of the full-potential-linear-augmented-plane-wave (FLAPW) method and the generalized gradient approximation (GGA). Nine independent elastic distortions of the unit cell were employed to determine the anisotropic elastic constants. Internal atomic relaxations after elastic distortions have been shown to have significant effects on the numerical values of elastic constants. Polycrystalline elastic moduli were determined from the elastic constants and were compared with that extrapolated from experimental data. The nature of chemical bonding and the electronic charge density distribution in TiB have also been explored to explain the high hardness and high stiffness values as well as the nature of elastic anisotropy.