An electron beam passing through a gas ionizes the gas, and the electrons and ions so produced collect in the vicinity of the beam to form a plasma with a number density that can be much greater than the density of the beam. A one‐dimensional static theory for such a system, with a beam either partially or completely filling the space between two parallel planes, gives the plasma density and potential distribution in the space. The theory requires only minor modifications of the Langmuir‐Tonks free‐fall theory of the positive column. A plasma filling the space occupied by the beam is separated by a low potential sheath from a somewhat lower density plasma that extends to the walls where a second higher potential sheath is formed. A comparison between the results of this theory and some density measurements on beam‐generated plasmas reported in the literature gives reasonable agreement.