Unintended and unwanted high frequency motion is sometimes observed in small-scale experimental works and in numerical simulations when soil is subjected to simple harmonic input motions. This high frequency motion has been often attributed to the drawbacks of actuating systems in experimental setups and to numerical noise in computational analyses. This work presents introductory consideration supporting the hypothetical idea that the recorded and the computed high frequency motion can possibly be the consequence of an unrecognized before physical phenomenon of soil elastic waves released in nonlinear hysteretic soil and affecting the dynamic response of soil to harmonic excitation. To this aim, simplified numerical studies representative of the most basic soil mechanical properties are carried out. The results reveal potential importance of soil-released elastic waves and their reflections inside a soil column when understanding the free field response in the numerical simulations representative of small-scale experimental setups. Chosen numerical cases are compared with available examples of experimental works from the literature. In addition, two further cases are analyzed, including a case showing the potential importance of soil-released elastic waves in the response of soil to real earthquakes, and a case showing the response of structural elements.