A fundamentally new digital model of the Earth’s lithosphere, which has no analogs in the practice of geophysical research, is described. It is a computer database (DB) of geophysical characteristics of the lithosphere processes, including geodeformation indicators. To study these characteristics, a specialized program was developed that allowed, using DB, to implement at a detailed and qualitative level models for analyzing, assessing and predicting the geophysical characteristics of the lithosphere, geodynamic risk, as well as justifying geodynamic indicators of the location of hydrocarbon deposits. The assessment of geodynamic risk is based on the use of a mathematical indicator, which is the spatial distribution of the values of the rotor of the full displacement vector in the geological environment. The proposed mathematical models, numerical methods, and algorithms open up new prospects for conducting scientific research both in the field of managing complex distributed territorial systems and in solving practical problems of analyzing, assessing, and predicting geodynamic risks and searching for hydrocarbon deposits.