Titanium carbide (TiC) has a wide range of engineering applications such as structural components, protective coating materials for cutting tools and strengthening phase because of such superior properties as high wear resistance, high hardness, and good chemical resistance. However, the intrinsic failure mechanism of TiC remains unknown, which limits its extended engineering applications. Here, we used density-functional theory (DFT) at the Perdew-Burke-Ernzerhof (PBE) level to examine the shear-induced failure mechanism of TiC along various plausible slip systems. We found that the (110)[1 10] slip system has the lowest critical shear strength under both pure shear and indentation stress conditions, suggesting that it is the most plausible failure system under both conditions. The failure mechanism arises from the Ti-C bond stretching and finally breaking with the increase in shear strain. The deformation modes along other possible slip systems are also investigated, which illustrate the failure mechanism along other slip systems. Our results provide atomistic explanation of the brittle failure of TiC, which will be useful for designing TiC based hard materials with improved mechanical properties.