A model of the electrons in a metal or a plasma in which they are regarded as forming a gas that interacts with a uniformly distributed background of positive charge to ensure that the system is electrically neutral. The electron gas is analysed theoretically using either classical or quantum statistical mechanics and the kinetic theory of gases. The electron-gas model accounts for many properties of metals and plasmas in a qualitative and approximately quantitative way but cannot give an accurate quantitative account of these systems, as this would require the motions of the positive ions to be taken into account.