Three kinds of models are used for beam instability analyses: those based on a solid beam, an infinitesimally thin annular beam, and a finitely thick annular beam. In high-power experiments, the electron beam is an annulus of finite thickness. In this paper, a numerical code for a sinusoidally corrugated waveguide with a finitely thick annular beam is presented and compared with other models. Our analysis is based on a new version of the self-consistent linear theory that takes into account three-dimensional beam perturbations. Slow-wave instabilities in a K-band oversized sinusoidally corrugated waveguide are analyzed. The dependence of the Cherenkov and slow cyclotron instabilities on the annular thickness and guiding magnetic field are examined.