The vibration interaction between the top-plate of buried VS 1.6 and VS 2.2 plastic, anti-tank landmines and the soil above it appears to exhibit similar characteristics to the nonlinear mesoscopic/nanoscale effects that are observed in geomaterials like rocks or granular materials. In nonlinear detection schemes, airborne sound at two primary frequencies f1 and f2 (chosen several Hz apart on either side of resonance) undergo acoustic-to-seismic coupling. Interactions with the compliant mine and soil generate combination frequencies that, through scattering, can effect the vibration velocity at the surface. Profiles at f1, f2, f1-(f2-f1) and f2+(f2-f1) exhibit a single peak while profiles at 2f1-(f2-f1), f1+f2 and 2f2+(f2-f1) are attributed to higher order mode shapes. Near resonance the bending (softening) of a family of increasing amplitude tuning curves (involving the surface vibration over the landmine), exhibits a linear relationship between the peak particle velocity and corresponding frequency. Subsequent decreasing amplitude tuning curves exhibit hysteresis effects. New tuning curve results for buried M 14 and VS 50 plastic anti-personal landmines along with experiments with a buried “plastic drum head” mine simulant behave similarly. Slow dynamics explains the amplitude difference in tuning curves for first sweeping upward and then downward through resonance, provided the soil modulus drops after periods of high strain.