A model for the enhanced conduction induced in dielectric films under electron bombardment while electrically stressed is discussed. It is assumed that the beam produces a virtual electrode at the end of its range in the dielectric and, as a consequence, the induced conduction is shown to depend on the properties of that part of the dielectric beyond the range of the beam. This model has also been discussed recently by Nunes de Oliviera and Gross. In the present treatment, it is shown how the model permits investigation of beam scattering and carrier generation and recombination processes. Experiments on electron-bombardment-induced conduction of thin (72 to 360 nm) films of anodic tantalum oxide are reported and it is shown that the theoretical model provides a very satisfactory explanation of all features of the results including the apparent threshold energy for enhanced conduction.