Problems associated with wellbore instability are one of the main causes of high costs and operational challenges in the oil and gas industry. Numerous geomechanical modeling techniques have been developed to address these issues. However, the existing models are limited due to the fact that they fail to account for the inherent variability of the rocks's mechanical and petrophysical properties, as well as the uncertainty in the values for the rock properties and other critical input parameters. This paper describes the adaptation of probabilistic techniques for performing a wellbore stability analysis in order to quantify the model uncertainty and improve the predictions made. This technique involves the use of a probabilistic approach that captures uncertainty in input variables through running a Monte-Carlo simulation to calculate the safe mud weight window as a probability distribution. A sensitivity analysis is also carried out by using once at time method (OAT) to identify the most significant input parameters. Results of the analysis illustrated that various uncertainties of input data based on measurement errors from well log tools are the main source of uncertainty in some key influential parameters used in wellbore stability models. The methodology presented here can be used as a pre-drilling design tool to predict optimal mud weight windows for a better drilling program.