The cherenkov and slow cyclotron instabilities driven by an axially injected electron beam in a cylindrical waveguide are studied using a new version of the self-consistent linear theory considering three-dimensional beam perturbations. There are three kinds of models for beam instability analysis, which are based on a cylindrical solid beam, an infinitesimally thin annular beam, and a finitely thick annular beam. Among these models, the beam shape properly representing the often used actual annular electron beams is the finitely thick annulus. We develop a numerical code for a cylindrical waveguide with a finitely thick annular beam. Our theory is valid for any beam velocity. We present eigen-modes of the cylindrical system with the plasma and beam. Instabilities driven by the annular beam in a dielectric-loaded waveguide are also examined.