The energy band structure of AGNRs can be obtained by making the transverse wavenumber discrete, in accordance with the edge boundary condition, which is analogous to the case of carbon nanotubes where periodic boundary conditions apply [172]. An analytical model for the dispersion relation and the wave functions of AGNRs is presented in Ref. [168]. However, because in ZGNRs the transverse wavenumber depends not only on the ribbon width but also on the longitudinal wavenumber, the energy band structure cannot be obtained simply by slicing the bulk graphene band structure. Therefore, exact analytical models can not be derived for ZGNRs [172]. In this chapter, we present two approximations for the wavenumber of ZGNRs which result in simple analytical expressions for band-structure and wave functions. We show that the analytical model is valid for a wide range of GNR indices.