The stability of coal pillars remains one of the most important practical problems for ensuring the geodynamic safety of underground mining. Stress enhancement in the vicinity of openings is responsible for the manifestation of rock, coal and gas bursting, the unsustainability of protective pillars, etc. Stress-induced damage of pillars occasionally causes the breaks of mining due to outbursts. In this work, we apply the finite-difference continuum damage mechanics approach to modeling stress-strain evolution of the rock mass during extraction of adjacent longwall panels of an inclined seam. The numerical modeling allows for explicit account of many factors affecting the rock massif behavior. These are gravity forces, lithology, tectonic stresses, natural discontinuities, geotechnical and mining parameters, etc. When the model parameters are calibrated against the on-site observations, the results of numerical modeling provide a reliable basis for pillars stability assessment. We build a structural model of a rock mass containing an underground working on the basis of a simplified stratigraphy of the Kondomsky deposit, Kuznetsky coal basin, Russia. Based on the results of numerical modeling, the stability of protective pillar is analyzed.