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Borehole breakout initiation, progression, and stabilization are modeled using a semi-analytical method based on Melentiev’s graphical conformal mapping procedure, and Kolosov–Muskhelishvili complex stress potentials. The only input data required are the elastic moduli of the rock, the Coulomb strength parameters (cohesion and angle of internal friction), and the far-field stresses. The stresses around the borehole wall are computed, the region in which the rock has failed is then “removed”, creating a new borehole shape. This process is iterated until a shape is obtained for which the breakout will progress no further, and a stable state has been reached. This modeling shows that stresses around the flank of the breakout evolve so as to reduce the propensity for shear failure, which helps to explain why the breakout width remains relatively constant throughout the process, even as the breakout region deepens radially. The failed area around the borehole becomes smaller and more localized, as the breakout tip sharpens and deepens. Using the Mogi–Coulomb failure criterion, a good match is obtained between the modeled breakout geometry and the geometry observed by Herrick and Haimson in laboratory experiments on an Alabama limestone. The new method leads to a correlation between breakout geometry, rock strength properties, and in situ stress. The paper ends with a critical discussion of the possibility of inferring the in situ stress state from observed breakout geometries.