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A theoretical study was carried out by first‐principles calculations using plane‐wave pseudopotential method to investigate the crystal structures, relative stabilities, and elastic properties of seven known titanium dioxide (TiO2) polymorphs. Our calculated equilibrium structural parameters of TiO2 polymorphs are in good agreement with the experimental results. Firstly, it is worth to note that from our energy‐minimized generalized gradient approximation (GGA) calculations, the four phases of TiO2 – anatase, rutile, columbite, and baddeleyite – are seen to lie within a very close energy range (0.02 eV/atom) of each other, which implies easy phase transition between them. Secondly, on the basis of enthalpy versus pressure data obtained from our GGA calculations for high‐pressure forms, we demonstrate the phase transition pressure and the expected sequence of the phase transition of TiO2, which are in reasonable agreement with experimental observations. Finally, we calculate the elastic constants of all the TiO2 polymorphs, and based on them, the bulk modulus, shear modulus, Young's modulus, and Poisson's ratio are estimated. The results show that cotunnite‐type TiO2 is a potential low‐compressible material.

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