The finite element method of stress analysis was utilized throughout this study to model single- and double-entry longwall systems. The influence of the geology, mining depth and mine-layout on barrier pillar stability was examined and design guidelines for determining sizes for such pillars were established using the "pillar core concept". The yield zone was better estimated by the use of the Coulomb failure/strength approach than the Drucker-Prager failure criterion. The width of the yield zone surrounding a barrier pillar is not constant as originally assumed, but depends on the size of the panel width (width of extraction). However, its influence can be ignored for face lines in excess of 800 feet. Although this analysis was based on information pertaining to a particular mine plan and specific geologic conditions, the recommended values of pillar sizes are in agreement with those suggested in other case studies. The results presented in this thesis, therefore, could serve as a general approximation of barrier pillar sizes if a more precise analysis is not available. / M.S.