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Because coal resources are dwindling, it is necessary to mine seams that are more difficult to support structurally. The mining industry needs a mine layout that is safe, but designed to be competitive in the world market. Presented in this dissertation is a technique that predicts the stress distribution in coal mine pillars. This approach uses an analytic equation to predict stress and yield characteristics; so, in some respects, it is as accurate as numerical modeling. It uses fracture mechanics to model many structures including longwall gob, yield pillars, cribs, posts, longwall chocks and hydrostatic loads. It models the yield characteristics of the coal seam by combining empirical pillar strength equations into the analytic analysis. The method is simple and quick which makes it attractive for stress analysis software. It should be more accessible to those in the mining industry who do not have expertise in rock mechanics or numerical modeling. Even though the purpose of this research is for modeling coal mines, it should be adaptable to any mine in a tabular deposit. A variation of the method may be applicable in other areas of engineering such as fluid flow, mine ventilation, network analysis, heat transfer, and earthquake applications.