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The failure criterion is a very important aspect of the wellbore stability analysis. But the Mohr–Coulomb criterion, a most commonly used failure criterion, is usually too conservative, due to the influence of the intermediate principal stress is not taken into account. Furthermore, the safe mud weight (MW) predicted by the conventional method is usually too high, due to the safe MW is predicted to yield no shear failure around the borehole. To solve the above problems, a semi-analytic model of wellbore stability analysis was proposed based on the stress distribution model, failure criteria and the breakout width model. The Mogi–Coulomb criterion, a new true-triaxial failure criterion, is involved in this semi-analytic model to determine the shear failure. The computational models of the lowest and highest safe MW are derived for different failure mode. The numerical method and flowchart of this semi-analytic model is provided, and a computer program is also developed in Matlab software. The impacts of the failure criteria, stress regimes and breakout width had been systematically analyzed. The optimal well path had been optimized for different stress regimes. The results showed that the lowest safe MW predicted by Mogi-Coulomb criterion is always lower than the Mohr-Coulomb criterion. The most stable drilling direction is along the minimum horizontal stress for the NF and NF–SS stress regimes, while it’s along the maximum horizontal stress in the SS, SS–RF and RF stress regimes. If the breakout width model is used, the lowest safe MW is always lower than the traditional method. The optimal well path and the wellbore stability are different between traditional and new methods. The most stable path is always the horizontal and deviated well for the traditional method, instead, it’s always the vertical well for this new method, it’s more consistent with the actual situation. These results also illustrated that an acceptable breakout is usually allowed to occur in the actual borehole, and the borehole still has enough arc to support the wellbore wall and to prevent collapse accident. Finally, both of the traditional and new methods are applied in the field case studies. The results showed that the lowest safe MW predicted by the integration of the breakout width model and Mogi–Coulomb criterion is closest to the real MW, instead, the lowest safe MW predicted by the traditional methods has exceeded the actual MW. It also illustrated the traditional method is too conservative in predicting wellbore stability, while this new method is more accurate for the integration of the breakout width model and MG–C criterion. This research can provide support to optimize the well path and MW in the drilling practices. [ABSTRACT FROM AUTHOR]