Abstract A method for estimating the borehole pressure or mud weight, required for maintaining the stability of a deviated wellbore, is presented in this paper. The critical borehole pressure is calculated by incorporating elastic stresses on the hole surface into a failure criterion of the rock. The Drucker-Prager criterion together with an experimentally obtained Mohr-Coulomb (p - q) curve is used to estimate the condition for plastic flow on the hole surface, and the maximum tensile stress failure criterion is applied to calculate the breakdown pressure of the hole. Both the flow induced stresses and the effect of pore pressure on failure of rock are taken into consideration. It is demonstrated that the plastic failure of borehole is very sensitive to the pore pressure, and that the range of safe borehole pressures (or mud weights) decreases with the increase of the borehole inclination angle.