The spatiotemporal development of electron and positive‐ion densities, electric field, and luminosity are calculated for electron‐pulse experiments in parallel‐plane gaps by numerically solving continuity equations together with Poisson's equation. Experimental coefficients for electron transport, cathode photoemission, and gas photoionization are used. The results show that anode‐ and cathode‐directed ionizing waves, or streamers, develop from the electron‐pulse‐initiated avalanche when it reaches midgap, and produce a weakly ionized plasma. Both filamentary plasmas and uniform plasmas that fill the interelectrode volume have been experimentally observed. Calculated and experimental streak photographs agree well in both cases. In filamentary discharges, a return ionizing wave also propagates from the anode when the anode‐directed wave arrives. The results show that electrons must be present ahead of the wave for cathode‐directed wave propagation. These electrons are supplied by photoionization, photoemission, or both depending on the experimental conditions.