As a result of its steplike density profile, combined with the monotonically increasing dipole magnetic field close to the Earth, compressional waves propagating outside the plasmapause can tunnel through and be trapped in a narrow layer that acts as a potential well. The spectrum and the spatial structure of these resonant localized modes are discussed for representative plasmasphere parameters. Data from Sub‐Auroral Magnetometer Network, British Geological Survey, and International Monitor for Auroral Geomagnetic Effects station pairs are used to infer representative density profiles in the plasmasphere. These data are then used to analyze the existence and properties of trapped compressional modes near the plasmapause.