Self‐consistent equilibria of cylindrical beams are studied in the Vlasov framework with the assumption of a uniform canonical axial momentum for the particles. The study is restricted to beams of circular cross section without azimuthal currents, but not necessarily without axial magnetic field. Attention is focused on beams with intensities much higher than Alfve´n’s limit, which are shown to progress slowly along the axis and to flow predominantly in their external sheath.