We have studied the structural, electronic, and mechanical properties of TiCxOy, using first principles calculations based on the density functional theory and pseudopotential method, within the generalized gradient approximation for the exchange-correlation functional. These calculations provide the lattice parameter, density of states, cohesive energy, elastic constants, and moduli as a function of carbon and oxygen content. The calculated values of lattice parameters and elastic moduli are generally in good agreement with experiments and compare well with other theoretical results.