A failure criterion for coal is proposed in which a distinction is made between brittle and "pseudo-ductile" failure. This criterion is then used in the development of new equations for coal pillar strength, including a transition from brittle fracture to pseudo-ductile yielding. In addition, equations are obtained which allow the ritical minimum pillar dimensions to be calculated to avoid "catastrophic" and "ultimate failure". The use of these formulae is then demonstrated by comparing the results with pillar case histories derived from the literature.