[en] We have carried out electronic structure total energy calculations on rhenium in the hexagonal close packed (hcp) and body centred cubic (bcc) phases, by the full potential linear muffin-tin orbital method, in order to verify the stability or the ambient pressure hcp phase against transition to the bcc structure at high pressures. As per our results, no hcp to bcc structural transition can occur up to 1 TPa pressures. Moreover, our Bain path calculations show that face centred cubic and body centred tetragonal structures are also not energetically preferred over hcp in this pressure range. The axial ratio (c/a) or Re changes by less than 0.33% in the pressure range studied. (author)