Source localization is an important structural health monitoring task, yet traditional localization techniques struggle due to complex geometries, dispersive wave propagation, and structure–medium coupling. This study applied matched field processing (MFP), a source localization technique developed for underwater acoustics, to localize impact sources on metal plates using remote acoustic measurements of airborne sound in conjunction with a physics-based acoustic-wave propagation model. A linear array of 14 microphones recorded radiated sound from a stainless-steel ball bearing dropped onto a 0.64 cm–thick, 91.4 cm–diameter aluminum plate in the nominal 5–20 kHz bandwidth. Physics-based finite element models were developed for both infinite and finite plates. The infinite plate model emphasized generic sound radiation with proper time-windowing, while the finite plate model included edge reflections specific to the plate studied. Both models achieved localization errors within 0.5 cm when data were temporally trimmed to accommodate model constraints. In environments with additive Gaussian noise, the finite plate model maintained greater than 80% localization accuracy down to a signal-to-noise ratio of –7.5 dB. Results further showed that MFP is robust to moderate mismatches in source characterization, but deviations in sensor location approaching a half-wavelength and deviations in plate thickness approaching 10% can reduce localization accuracy.