The equation of state, structural behavior and phase stability of α-uranium have been investigated up to 1.3 TPa using the density functional theory, adopting a simple description of electronic structure that neglects the spin–orbit coupling and strong electronic correlations. Comparison of the enthalpies of Cmcm (α-U), bcc, hcp, fcc and bct reveals that the α-U phase is stable up to a pressure of ∼285 GPa, above which it transforms to a bct-U phase. The enthalpy differences between the bct and bcc phases decrease with pressure but bcc is energetically unfavorable at least up to 1.3 TPa, the upper pressure limit of this study. The enthalpies of the close-packed hcp and fcc phases are 0.7and 1.0 eV higher than that of the stable bct-U phase at a pressure of 1.3 TPa, supporting the wide stability field of the bcc phase. The equation of state, the lattice parameters and the anisotropic compression parameters are in good agreement with experiment up to 100 GPa and previous theory. The elastic constants at the equilibrium volume of α-U confirm our bulk modulus. This suggests that our simplified description of electronic structure of uranium captures the relevant physics and may be used to describe bonding and other light actinides that show itinerant electronic behavior especially at high pressure.