First-principles calculations using plane-wave basis sets and ultrasoft pseudopotentials have been performed to study the mechanical stabilities of the rutile, pyrite, fluorite and cotunnite phases of titanium dioxide (TiO 2 ). For these polymorphs, we have calculated the equilibrium volumes, equations of state, bulk moduli and selected elastic constants. Compared to the three phases rutile, pyrite and fluorite, the recently discovered cotunnite phase shows the highest c 44 for all pressures considered. Cotunnite also shows the highest bulk modulus amongst the four studied phases at an ambient pressure of B 0 = 272 GPa.