Borehole stability analysis plays an important role in the design of oil and gas well drilling. A main aspect of borehole stability analysis is the selection of an appropriate rock strength criterion. The two most commonly used rock strength criteria in borehole stability analysis are the Mohr-Coulomb criterion and the Drucker-Prager criterion. However, the Mohr-Coulomb criterion ignores the effect of the intermediate principal stress and is too conservative in estimating the critical overbalance pressure required to maintain borehole stability; while the Drucker-Prager criterion overestimate the effect of the intermediate principal stress and may result in non-sensible stability predictions. In this paper, a simple model based on a three-dimensional (3D) Hoek-Brown strength criterion is developed for stability analysis of vertical boreholes. Examples are presented to show the application of the 3D Hoek-Brown strength criterion for analyzing the stability of vertical boreholes and the results are compared with those using the Mohr-Coulomb and Drucker-Prager criteria. It shows that the 3D Hoek-Brown strength criterion predicts critical overbalance pressure values that are less conservative than those predicted by the Mohr-Coulomb criterion yet are not as unconservative as those predicted by the Drucker-Prager criterion.