In this paper, the effect of pressure on various properties of brookite and rutile TiO 2 has been investigated along with a phase transition study. It is seen that brookite gets transformed to rutile TiO 2 at 5 GPa pressure. The bandgap of brookite and rutile TiO 2 are direct in nature with values of 3.41 eV and 2.98 eV. Pressure-dependence of the Elastic compliance coefficients, elastic stiffness coefficients, bulk modulus, shear modulus, Young modulus, Poisson's ratio, B/G ratio, Vickers hardness, Lame constant has been calculated at 0, 3, 5 GPa pressures for brookite TiO 2 and at 0, 5, 10, 15, and 20 GPa pressures for rutile TiO 2 . The shear anisotropy factors (A 100 , A 010 , and A 001 ) along {100}, {010}, and {001} planes have been estimated at different pressure for brookite TiO 2 as well as the shear anisotropic factors along {100} and {001} shear planes is estimated for rutile TiO 2 . Moreover, anisotropy factors (A B ), (A G ), and (A U ) have been estimated at different pressure for brookite TiO 2 and rutile TiO 2 . Furthermore, the dielectric constant is determined to investigate other optical properties for both the structures at different pressures. A pretty good agreement has been obtained between our findings and experimental data.