Core holes are an important contributing factor to the core-loss fine structure in electron energy-loss spectroscopy (EELS). While there has been much work on bulk materials, less is known about core hole screening in more complex dielectric environments, such as free surfaces or interfaces between two different materials, even though the latter is frequently encountered in high spatial resolution EELS analysis. In this work, experimental O K- and Mg L3,2-EELS edges from the free surfaces of a MgO cube are measured using scanning transmission electron microscopy (STEM). The free surface O K-spectrum shows extra intensity at the edge onset compared with the “bulk” spectrum. Core hole screening near a free surface is modeled using electrodynamic theory. It is shown that much of the extra intensity is due to reduced core hole screening, while genuine surface states make a smaller contribution to the fine structure. The low energy Mg L3,2-edge, however, does not show any significant change at a free surface. This is because the measurement is less surface sensitive due to strong delocalization.