Stress-induced failure is among the most common causes of instability in Canadian deep underground mines. Open stoping is the most widely practiced underground excavation method in these mines, and creates large stopes which are subjected to stress-induced failure. The probability of failure (POF) depends on many factors, of which the geometry of an open stope is especially important. In this study, a methodology is proposed to assess the effect of stope geometrical parameters on the POF, using numerical modelling. Different ranges for each input parameter are defined according to previous surveys on open stope geometry in a number of Canadian underground mines. A Monte-Carlo simulation technique is combined with the finite difference code FLAC3D, to generate model realizations containing stopes with different geometrical features. The probability of failure (POF) for different categories of stope geometry, is calculated by considering two modes of failure; relaxation-related gravity driven (tensile) failure and rock mass brittle failure. The individual and interactive effects of stope geometrical parameters on the POF, are analyzed using a general multi-level factorial design. Finally, mathematical optimization techniques are employed to estimate the most stable stope conditions, by determining the optimal ranges for each stope’s geometrical parameter.