A special model of vertically loaded pillar behaviour is introduced to the general, multi-plate based, floor-pillar-roof system interaction analogue. This permitted analysing room-and-pillar mine systems in any geological conditions, including the effect of pillar elastic-plastic behaviour with strain softening. In the model, pillar instability is one of the important phenomenon, which may be expected to occur, and which the operator has to be prepared for. Thus the entire system's safety is determined mainly by strong roof strata behaviour and therefore they have to be examined in actual stress-strain conditions utilising the appropriate strength theories. It was assumed that the so-called safety margin, representing the relation between load intensity and material strength, might serve as the basic indicator of possible roof instability development. Therefore, the safety margin may be estimated by comparing the actually computed components of stress-strain tensor with ultimate values characteristic for a given material determined in laboratory. In order to illustrate the effect of technological pillar size on roof strata stability, two different mining systems (methods of mining) in one of the Polkowice-Sieroszowice' Mine districts was modelled using the finite element method formulated in three dimensions, assuming different materials within different rock mass strata, as well as a number of horizontal planes of discontinuity within the model.