Abstract <p>The article is devoted to improving the method for predicting seismograms and accelerograms of strong ground movements under the assumption that an earthquake is an instantaneous rupture of the Earth’s crust. The method makes it possible, using the obtained theoretical formulas, to calculate the values of all three ground movement parameters—displacements, velocities, and accelerations—during strong earthquakes with magnitudes of <i>M</i> ≥ 6.0 for general inhomogeneous (multilayer) soil foundations. The article considers cases of inhomogeneous two-layer foundations. The results obtained for 16 variants of heterogeneous two-layer construction sites of categories I–IV based on seismic properties with magnitude <i>M</i> = 7.0 and distance of 15 km from the line of rupture of the predicted earthquake are given as an example. Comparison of the results obtained for real heterogeneous foundations with equivalent homogeneous foundations showed up to 1.3–1.6 times of discrepancies towards an increase, depending on the number of five or three modes of higher oscillations taken into account. Significant influences of various modes of natural oscillations of foundations on the values of displacements and accelerations on the ground surface of a heterogeneous foundations compared to a homogeneous foundation have been revealed. A significant decrease (two or more times) in the rigidity of the upper layer, compared to the rigidity of the lower layer, leads to a significant increase in accelerations on the ground surface. It is recommended that for heterogeneous foundations, the predicted values of displacements and accelerations should be implemented taking into account at least five modes of oscillations of the soil foundation.</p>