Problems of predicting displacement and acceleration values for strong ground motions are considered for the case when an earthquake is assumed as an instantaneous mechanical break of the Earth surface. The purpose of the studies is an attempt to develop, based on the up-to-date concepts of earthquake generation process, simplified theoretical methods for the quantitative prediction of ground motion parameters in strong earthquakes. The case considered as an illustrative example is that of an earthquake originating as a consequence of relatiemotions of suddenly ruptured blocks in horizontal direction with a given initial velocity. The work established an empirical relationship between the soil particle motion velocity near the rupture, at certain distance from it, on one hand, and the earthquake magnitude, on the other hand. It is assumed that given the instantaneous break of a medium, the impact of inertial motions of deep soil strata on the inertial motions of upper, subsurface soil strata can be neglected. By solving wave task for a multi-layer near-surface stratum, analytical relations were produced for soil seismogram and accelerogram on the Earth surface depending on: the physical-mechanical and dynamic characteristics of soils in all layers of the stratum; attenuation ratios of mechanical soil vibrations; distance to the rupture; and, magnitude of the predicted earthquake. The obtained results enable establishing not only peak ground displacement and acceleration values with allowance for local soil conditions, but also their changes in time, and, the value of predominant soil vibration periods. The method is illustrated for the rocky and soft soil basements. On the basis of the results obtained (17), a technique for determining soils’ synthetic accelerograms of the soils of predicted strong earthquakes with a M?6.0 magnitude has been developed for various construction sites of seismic properties with a T01 dominant period from 0.1 to 2 sec. The method is illustrated for hard and loose ground bases, with 6.0?M?9.0 magnitudes (see Tables 3 and 4, and Figures 3 and 4). Quantitative assessments of the base higher forms vibration influence on the values of displacements and accelerations are given. It is shown that these values increase the acceleration of soils 2.53 times when calculated only by the first form, and by movement only 1.1 times. When the magnitude of the predicted earthquake changes by only one unit then displacement and acceleration of soils are changed 2.72 times. The displacement and acceleration of soils during earthquakes of M = 6.0 magnitude are 20 times less than for earthquakes with magnitude M = 9.0. The displacements and accelerations of solid and loose soils at a distance ? = 15 km are approximately 2 times less than for the discontinuity (? = 0), regardless of the earthquake magnitude. Accelerations of solid soils running up to M?7.0 magnitudes can reach 1g, and on loose soils – only at M?8.0.