The radiation of a bunch of charged particles moving along the axis of a cylindrical waveguide lined with a resonant dispersive dielectric medium is theoretically studied. Conditions necessary for the amplification of generated waveguide modes are established. It is shown that any selected mode or a group of neighboring modes can be amplified provided that the system parameters are properly chosen. The maximum possible growth increment is independent of the mode number and is determined entirely by the properties of the resonant medium.