Covellite CuS consists of alternating layers with compositions CuS and Cu 2S 2. We examine the anisotropy of the electrical conductivity and the origin of the structural phase transition in CuS by performing extended Hückel tight-binding band electronic structure calculations. Our study shows that CuS is a three-dimensional metal, but its conductivity should be much greater along the directions perpendicular than parallel to the c-axis. The partially empty valence bands of CuS have strong contributions from the sulfur 3p orbitals of the Cu 2S 2 layers, so that the oxidation state of CuS is better described by (Cu +) 3(S 2-)(S 2- than by (Cu +) 3(S -)(S 22-). The structural phase transition of CuS is not driven by Fermi surface instability. A probable cause for this phase transition cannot be the bonding interactions between the Cu + ions but the van der Waals interactions of the S…S contacts between the CuS and Cu 2S 2 layers.