The success of drilling operations strongly depends on proper mud weight design. In fact, unsuccessfully optimizing the mud weight could lead to wellbore collapse. Within the oil industry, Mogi and Mohr-Coulomb models are the most-practiced failure criterion used in predicting critical mud weight. This paper was aimed at inspecting these models regarding mud weight prediction. A new comparison concept was also developed. Furthermore, the different stochastic perspectives were carried out in the study. Based on field data, the required mud weight was found using the Mogi and Mohr-Coulomb failure criteria. The results suggested that the predicted pressure from the Mogi model is considerably close to the real mud weight. The study is also developed using the new pragmatic comparison criteria called the breakout width. The predicted mud weight from both models was separately utilized to obtain the width of shear failure (breakout) by applying the simple analytical model. The results revealed the breakout dimension was a bit over-predicted with respect to the Mohr criteria. Moreover, the optimum mud weight was a function of input parameters, which include stresses and rock properties. The knowledge of such parameters depends effectively on the quality of the parameters. The deterministic approach was presented to display the influence of each parameter by developing tornado diagrams. The analysis was defined that the maximum horizontal stress is the most influential parameter for collapse pressure prediction for both models. In addition, overburden stress has a considerable effect on the Mogi model and was ignored in the Mohr criteria. Other parameters were also captured in the analysis. In this paper, the probabilistic analysis approach using Monte Carlo simulation was also implemented into wellbore stability models to cover all the significant parameters with their uncertainties rather than certain values for improving predictions. Based on the analysis, the mud weight optimization will have a direct impact on future drilling practices and operation costs. © 2019, Society of Petroleum Engineers.