This research explores vibratory drum interaction with layered elastic media. The media considered in the study is soil. Field soil stiffness values from force-displacement loops measured during vibratory compaction on layered systems are compared to those computed using boundary element methods, equivalent linear and iterative equivalent linear dynamic finite element analysis procedures. It is found that the contribution of the underlying subgrade exceeds the contribution of the top layers in common configurations used in earthwork. The contact width profiles obtained from stiff soils match closely those predicted by Hertzian contact theory. The differences between the dynamic and pseudo-static analyses are significant and decrease at higher soil stiffness. The stiffness values predicted vary widely between the linear and nonlinear approximation with the differences becoming significant for soft media. Within the stated assumptions, the study shows that the dynamic analyses more closely predict the trends of the real-world values.