The vibrational population distribution for hydrogen molecules in a hydrogen discharge has been calculated taking into account electron collisional excitation, molecule‐molecule, and wall collisional de‐excitation processes. Electronic excitation processes include vibrational excitation by 1 eV thermal electrons acting through the intermediary of the negative ion resonances, and vibrational excitation caused by the radiative decay of higher singlet electronic states excited by a small population of 60 eV electrons in the discharge. The molecules are de‐excited by molecular collisions transferring vibrational energy into translational energy, and by wall collisions. The distributions exhibit a plateau, or hump, in the central portion of the spectrum. The relative concentration of negative ions is calculated assuming dissociative attachment of the low temperature electrons to vibrationally excited, non‐rotating molecules. The ratio of negative ions to electrons in the discharge is calculated to be of order 1% if the vibrational excitation survives no more than one wall collision, and of order 10% if the excitation survives ten collisions. The possibility is considered that the higher concentrations can be achieved with few wall collisions provided dissociative attachment occurs to highly rotating molecules.