The electronic and optical properties of the metallic bcc and β-Sn phases of tin are studied using density functional theory. The effects of spin-orbit coupling are examined and significant splittings are found in the band structures for both phases. Based on ab initio band structures we calculate the anisotropic optical response of β-Sn. Both intra- and interband contributions are included and the plasma frequencies for both the ordinary and extraordinary optical axis are calculated. The theoretical results are found to be in excellent agreement with experimental spectra for the anisotropic optical response. We identify the electronic transitions responsible for the dominant interband resonances in the near-infrared response.