Cherenkov radiation produced by an axial solid relativistic electron beam in a plasma filled dielectric lined slow wave waveguide was analyzed by the use of the self consistent linear field theory considering the three dimensional perturbation of electrons.The dispersion equation,which describes the instability,and the simultaneous condition of the beam wave interaction were derived.Finally,the growth rate of the wave was obtained,and the effects of the background plasma density and the electron beam radius on the growth rate of the wave were presented.