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Various theoretical studies have been done to investigate the structural parameters and electronic bandgap as well as optical properties using different techniques. In this study, we present structural and electronic bandgap of anatase and rutile titanium dioxide investigations by applying ultrasoft pseudo-potential plane wave approach developed within the frame of density functional theory (DFT) embodied in CASTEP computation program. We used generalized gradient approximation (GGA) by Perdow-Burke-Ernzerhof (PBE) for exchange correlation potential. In our investigations, geometry optimization is carried out for each calculation and subsequently related structural parameters and band gap of anatase (figure 1 (a, b)) and rutile (figure 2 (a, b)) titanium dioxide under different values of stress have been calculated. From our band structure analysis under stress we found different behavior of band gap between anatase (figure 1 (b)) and rutile (figure 2 (b)) titanium dioxide. The conduction band of anatase TiO2 moves opposite to the conduction band of rutile TiO2 as we increase the stress (equivalent to hydrostatic pressure). The parameters (V0, B0 and B0) of equation-of-state calculations to have been performed to obtain the zero pressure equilibrium volume. For unstressed anatase and rutile TiO2, our investigated lattice parameters, equilibrium volume (V0), bulk modulus (B0), pressure derivative of bulk modulus (B0) and bandgap results of anatase (fig. 1(a)) and rutile (fig. 2(a)) phases show significant improvements over earlier theoretical results [1-7]. Phases, anatase and rutile TiO2 are strong stable structures under stress.