We consider the average injection rate from a metal electrode into disordered organic media, and its field dependence for a fixed density of carriers in the metal. At sufficiently high field the injection occurs through particular pathways, lowering the energetic barrier between the metal Fermi energy and the molecular levels of the organic layer. Assuming a Gaussian distribution of random energies, we find the dependence of current j on field E j proportional to exp(beta root E) in the relevant domain of electric fields. This behavior agrees both with numerical simulations of three-dimensional systems and with experimental data.