A U.S. Bureau of Mines case study of pillar recovery in high-grade ore near the Ross shaft at, the Homestake Mine, Lead, SD, has demonstrated the usefulness of the finite-clement method for the evaluation of shaft pillar mining plans and shaft stability. This report, one of three in a series describing the Ross shaft pillar case study, focuses on the premining stability analysis. The two-dimensional computer program UTAH2 was used in advance of pillar mining; results suggested that the shaft would remain stable. Subsequent reports describe parts 2 and 3 of the study. In part 2, borehole extensometers and other instruments were installed to provide data for model verification and shaft monitoring. Results of the recalibrated two-dimensional model confirmed the premining stability evaluation. However, after mining began, great concern developed because of the appearance of cracks and other signs of ground movement over considerable distances from the area of active pillar miping. In part 3, an intense three-dimensional modeling effort using UTAH3 was initiated. The results again showed that the shaft would remain safe. Three-dimensional analyses of alternative pillar mining scenarios indicated that more of the shaft pillar ore reserve could be recovered than previously thought.