<p>The paper presents mathematical (computer) modeling. The research focuses on unsteady waves arising in a slab with different foundation configurations. The slab is in an elastic half-plane under seismic action. Devising methods for monitoring wave processes during the transient period is a relevant scientific objective. For this purpose, a technique, an algorithm, and a software system were developed. They enable obtaining stress tensor components, displacements and their derivatives in deformable bodies of various shapes under unsteady wave impacts. The developed technique was tested for reliability by solving problems of the impact of pulses in the form of a period of triangle, trapezoid, and sine waves. Seismic action on a system with a base which can be a spread footing or a pile foundation was also simulated. As a result, new data on contour stresses on the free surface of a slab were obtained.</p>