The complex deformation processes (stress-strain) are revealed in the title mentioned region. It is shown that the structure of lithosphere (crust and mantle tops), determined by the seismographic methods, points to its separation into layers. The forces of buoyancy (gravitation) are possible mechanism of stress-strain observed. The results of study of three basic models of lithosphere viscosity and computations of stress state of lithosphere correlate with the data on mechanisms of mantle earthquakes and localization of the seismic events in lithosphere. Localization of tectonic stresses, related to lithosphere separation into layers, its lateral heterogeneity and buoyancy explain an unusual seismic activity in the mantle depths under Apennines.