The paper presents the results of modeling stress fields and analyzing the strength of the rock mass at the Yeniseiskiy site (Krasnoyarsk Region), selected for the construction of an underground research laboratory. Variants of boundary loading conditions along the model boundaries are substantiated, and the results of modeling the distribution of stress tensor components for four loading scenarios are presented, along with an assessment of rock mass stability using well-known strength criteria, including Hoek – Brown, Mohr – Coulomb, von Mises, and others. Regularities in the distribution of stress fields within the rock mass and differences associated with the tectonic conditions of the area are identified. It is established that the localization of zones of stress intensity concentration depends on the ratio of the principal stress components. Orientation of compression in the submeridional direction leads to an increase in stress intensity by 10-15 % relative to other modeling variants. Zones of anomalous stress intensity values are located within blocks as well as in the footwalls of tectonic faults. The models are characterized by high values of the potential energy of distortion in fault zones (as parts of the rock mass most susceptible to deformation) and at their intersections. Three-dimensional modeling makes it possible to identify effects that are weakly expressed in plane strain models. The results of geomechanical modeling are required for planning experiments in the underground research laboratory in order to refine the isolation properties of the rock mass during the disposal of high-level radioactive waste. Methodological approaches of three-dimensional modeling are applied by geomechanical and geotechnical services of industrial enterprises and other hazardous facilities (underground gas storage facilities, mineral deposits, etc.).