The article describes the numerical modeling results of the stress-strain behavior of a room-andpillar stoping system in honeycomb mine design including rib pillars with their angles cut off by vertical cylindrical stopes. The factors of safety are calculated for the pillars and enclosing rock mass with the excessive stresses and displacement in rock mass. The authors present a selected variant of the numerical stress-strain modeling of rib pillar with angles cut off by vertical stopes of cylindrical form in case of cellular arrangement of the stopes for the conditions of mining at the depths of 400 and 1000 m. The numerical calculation of the critical depths for using honeycomb mine structures is presented as a case-study of geological and geotechnical conditions of the Ilets rock salt deposit. The patterns of destructive loads are obtained in numerical models at different ratios of minimal widths of pillars and diameters of stopes.