In the paper on the basis of earthquake focal mechanisms joint analysis and fault-block tectonics a model of geodynamic regime of the southern slope and south-eastern dipping of the Great Caucasus is given. It is shown that the result of the stress distribution and corresponding right- and left-side movement along the system of reverse faults and discharges of common-Caucasian strike and transverse shear in South-Western and North-Eastern direction is the rotation of the individual units in clockwise and counterclockwise, move aside the individual blocks to the east, as well as a feat of blocks of Kura River’s valley to the north under the structure of Great Caucasus, thrust of Great Caucasus surface structures to the south along the system of common-Caucasians reverse faults and thrusts. Described features of the geodynamic model are reflected in local tension anomalies of the geomagnetic field, which precede the seismic tectonic shifts (earthquakes) with the appropriate mechanism, and in the space-time tension increments of the geomagnetic field, that characterize the stress-strain state of the environment in the studied area.