Abstract <p>Elastic half-space models are widely used in geophysics and road science. In road science, these models are most often used to study the stress-strain state of pavements, which are artificially created layered media on the surface of the soil and geological massif, the main task of which is to distribute and transfer the load from a moving vehicle and ensure the comfort and safety of the user, as well as the durability of the road. Taking into account the common properties of road pavement and geological environment, methods close to geophysical methods are becoming more and more widespread when assessing the condition of road pavements. In the article the method of harmonic analysis is applied, which is realized to calculate the main characteristics of the response of layered media to test shock loading. Calculations of the amplitude–frequency characteristic of displacements at the point of shock loading were performed, and the change of its shape depending on the elastic moduli of the half-space layers was analyzed. It was found that a&#xa0;decrease in the elastic modulus of intermediate layers forms a pronounced ‘plateau’ in the low-frequency response of displacements. Decrease in the elastic modulus of the upper layer of the medium leads to an increase in the amplitude of displacements as the frequency increases. An increase in the elastic modulus of the underlying half-space leads to the appearance of an inflection point localized in the region of 500 rad/s, separating the amplitude–frequency response of displacements into two sections. The obtained results can be used in the development of nondestructive testing methods for layered media, oriented on the recording and analysis of the displacement amplitude–frequency response.</p>