Site response analysis is a component of paramount importance in reliable seismic risk assessment in earthquake-prone zones. The theoretical approaches to derive the site free field response to earthquake excitation include linear elastic, equivalent linear elastic and nonlinear analyses. This work shows new evidence on advantages of using nonlinear site response in modelling shear wave propagation. The nonlinear approach is shown to be able to reproduce the presence of elastic waves released in soil of hysteretic-type nonlinearity when subjected to dynamic loading. Based on the recent findings a simple 2D numerical study of an ideal experimental setup is presented. Finally, potential consequences of the recent findings on wave propagation in soil experiencing nonlinear hysteresis-type behavior are briefly discussed regarding the seismic response in large earthquakes (e.g. Mexico City) and developments of novel conbined finite element and constitutive formulations.