This paper presents a tight binding and ab initio study of finite zig-zag nanotubes of various diameters and lengths. The vertical energy spectra of such nanotubes are presented, as well as their spin multiplicities. The calculations performed using the tight binding approach show the existence of quasi-degenerate orbitals located around the Fermi level, thus suggesting the importance of high-quality ab initio methods, capable of a correct description of the nondynamical correlation. Such approaches (Complete Active Space SCF and Multireference Perturbation Theory calculations) were used in order to get accurate ground and nearest excited-state energies, along with the corresponding spin multiplicities.