Deep drilling can lead to the encounter of complex geological conditions, with significant overburden pressure leading to a narrow safety window for mud density. In this study, we deviated wellbore instability conditions using the Mohr–Coulomb and tensile failure criteria, solving for collapse, shear, and fracture pressure using Newton’s method. The safe mud density window is defined between the maximum value of pore and collapse pressures and the minimum value of shear and fracture pressures. The analysis of the Anderson fault stress model, utilizing this method, enables a comprehensive investigation of how the safety mud density window varies with wellbore inclination and azimuth angles under various stress conditions. Additionally, applications in Chinese oilfields illustrate that this methodology can accurately calculate and analyze extremely narrow safety mud density windows at depths ranging from 2000 to 3000 m. In conclusion, this method enables rapid and accurate prediction of mud density limits, improving wellbore stability and reducing drilling risks.