The cyclotron maser instability for a solid relativistic electron beam propagating parallel to a uniform axial magnetic fieldB0?zis investigated. The stability analysis is carried out within the framework of the linearized Vlasov‐Maxwell equations. It is assumed that &ngr;/?≪1, where &ngr; is Budker’s parameter and ?mc2is the electron energy. Stability properties are investigated for the choice of equilibrium distribution function in which all electrons have the same value of total perpendicular energy, the same value of axial velocity, and a step‐function distribution in canonical angular momentum. The instability growth rate is calculated including a determination of the optimum value of the beam radiusR0for maximum growth. It is found that the maximum growth rate for a solid beam is comparable to the maximum growth rate for a hollow beam.