Pillar systems in mines are statically indeterminate systems. The paper presents the results of numerical investigations to evaluate the effects of panel dimensions on pillar loads. It is shown that pillar load in deep mines is strongly influenced by the lateral and vertical extent of extraction panels. The commonly applied tributary area concept does not account for these effects and is an oversimplification that has to be applied with caution. The effects of local pillar failures on stability of pillar workings are examined using simple models. It is shown that limiting panel dimensions by substantial barrier pillars can reduce the danger of regional pillar collapses and enhance overall mine stability.