Extraction of shale gas and oil has significantly benefited the US economy. However, the applied technology of hydraulic fracturing is inefficient and ecologically unsafe. Electrophysical underground pyrolytic conversion of oil shale kerogen in energy stock can solve these problems. This processing method is feasible due to treeing in rock volume. Treeing has been widely studied in insulation as a negative factor. With regard to oil shale this phenomenon is examined insufficiently despite the fact that in this application area it has its distinctive features and is crucial for the initiation of rock heating and its further conversion. This article describes the shale's dendrite morphology which is non-typical of conventional treeing in insulation. Features of the discharge structures' formation are associated with a change of oil shale conductivity by discharge and with a high degree of rock heterogeneity.