In the frames of model of 'rigid beam' the analytical description is given of stabilizing influence of complex of factors on the development of hose instability of relativistic electron beam under the condition of ion focusing. It is shown that the stabilizing factors may be the effect of phase mixture of beam particles trajectories, the presence of external longitudinal magnetic field, the appearance of tracking force by transportation of beam through the conducting waveguide which is caused by the action of electrostatic image of shifted ion channel inside the earthed waveguide on the beam, and the presence of 'narrow' ion channel.