Galactic cosmic rays (GCRs) and solar energetic particles (SEPs) charge the subsurface lunar regolith. The electric fields could be strong enough to affect surface and subsurface chemistry and perhaps even the ejection of charged dust. These fields could also drive subsurface currents that significantly affect the surface charge. In this study, we model the expected depth profile of energetic charged particle fluxes and the resulting depth profile of the electric field. For a nominal regolith conductivity of 10^-14 S/m, we find that a typical GCR spectrum contributes a maximum subsurface electric field of about 0.5 V/m. We predict that a large SEP event, like one of the events in October 2003, can create subsurface electric fields on the order of 100 kV/m. These subsurface electric fields could significantly affect the surface electric field and the surrounding lunar plasma environment, particularly on the lunar nightside and within permanently shadowed regions. We also describe how the chemical and physical characteristics of the regolith affect conditions required for dielectric breakdown. Finally, we consider how data from the Cosmic Ray Telescope for the Effects of Radiation (CRaTER) on-board the Lunar Reconnaissance Orbiter (LRO) can constrain our model.