The goal of this paper is, to examine the validity of tributary area method, which is used as an empirical mean to estimate pillar dimensions, in room and pillar mines, taking into consideration a safety factor. A two-dimensional, linear elastic, finite element model (Phase 2D) is created for a simple case of a uniform pattern of room and pillar mine layout, that is lying flat 1200 m below ground surface. Sensitivity analysis has been done to study the effect of horizontal-to-vertical stress ratio, K, on the maximum stress that pillar can sustain without failure. Four cases have been presented in this investigation (K = 0.5, 1, 1.5 and 2). The results reveal that, the maximum stress on the pillar increases as K increases. Alternatively, factor of safety deteriorates as mining depth (i.e., increase of K-value) increases. The results also show that displacements/convergence expand as mining depth goes down.