We present an angle-resolved photoemission spectroscopy study of the electronic structure of SnTe and compare the experimental results to ab initio band structure calculations as well as a simplified tight-binding model of the p bands. Our study reveals the conjectured complex Fermi surface structure near the L points showing topological changes in the bands from disconnected pockets, to open tubes, and then to cuboids as the binding energy increases, resolving lingering issues about the electronic structure. The chemical potential at the crystal surface is found to be 0.5 eV below the gap, corresponding to a carrier density of p=1.14 × 10(21)  cm(-3) or 7.2 × 10(-2) holes per unit cell. At a temperature below the cubic-rhombohedral structural transition a small shift in spectral energy of the valance band is found, in agreement with model predictions.