Problem statement: The strength of rock pillars in the presence of si ngle, persistent, natural discontinuities can seriously be compromise d and lead the pillar to collapse because of instability along the discontinuity itself. Approach: A specific analysis method for this kind of problem has been set up in this study to evaluate t he stability of pillars and to determine the dimens ion that this kind of pillar should have in order to gu arantee the minimum requested safety factor. Results and Conclusion: The objective is to determine the limit shear stre ss and the actual acting shear stress at 25 points distributed along the discontinuity in order to then be able to obtain the safety factor concerning collapse of the pillar along the discont inuity surface.