This paper examines modern tectonic processes and the state of stress in the North Caucasus along three profiles that cross its eastern, central, and western parts. Using the models of crustal structure along these profiles, we solved the following inverse problem: to find boundary conditions (in this study, velocity at side boundaries and bottom of the model) that provide the best fit of calculated vertical movements at the top of the model and vertical neotectonic movements during the late Quaternary. Our modeling shows that during the late Quaternary, geodynamics of the eastern and central parts has been controlled by regional intraplate compression normal to the Greater Caucasus belt. The western part has been strongly influenced by tectonic processes taking place in the Eastern Black Sea. The calculated slow flow patterns and stress fields showed good agreement with the distribution of seismic events, results of focal mechanisms inversions, and GPS data.