Experiments were performed measuring beam current, magnetic field, and energy of a 400‐keV relativistic electron beam propagation in air in a 7.6‐cm‐diam glass guide tube, the same covered with a conducting screen, and in a 3.4‐m‐diam chamber. Nose‐erosion rates, current neutralization, and stability data are given at various pressures. A propagation window exists between pressures of 270–1070 Pa. At the lower pressures, propagation is limited by nose erosion, whereas at higher pressures, propagation is limited by instability of the tail. The conducting screen stabilizes the tail of the beam, extending the high‐pressure end of the window to ∼6000 Pa. Rectilinear propagation within 5 mrad occurs in the large chamber at 270–800 Pa.