Wellbore instability is a critical and costly problem in the petroleum engineering industry, which has yet to be fully understood and addressed. This is mainly because of uncertainty in some key influential parameters, such as in situ stress, rock strength, and other engineering operating parameters. These can lead to wellbore stability uncertainty, and make it very difficult for the conventional deterministic approaches to predict the risks associated with the instability problems during the drilling and production process. To account for the uncertainty involved in the wellbore stability analysis, a Monte Carlo uncertainty analysis technique has been combined with a numerical geomechanical modelling method to develop a geostatistical approach. This makes it feasible to assess not only the probability of achieving a desired degree of wellbore stability at a given mud weight, but also the effects of the uncertainty in each parameter on the stability of the wellbore. This approach has been applied to a case study of a vertical well in deepwater. The most influential parameters have been identified by a sensitivity analysis technique, and the likelihood of avoiding wellbore failure in different modes is obtained across a range of mud weights. The advantage of adopting numerical methods in this study lies in more realistic geomechanical representations of the wellbore stability problem, and less uncertainty from numerical modelling compared with the analytical models used in previous studies. Results of the analysis illustrate the potential of the approach to be used as a pre-drilling design tool to predict optimal mud weight windows for a better drilling program.