I develop a simple technique to indicate the onset of stress-induced mechanical damage near a wellbore. Stress concentrations near a wellbore can cause the yield strength of the rock to be exceeded. The resulting mechanical damage causes a decrease in acoustic velocity that precedes the development of breakouts. With laboratory experiments on stressed boreholes, I show that high-resolution, shallow acoustic measurements made inside the borehole can detect these stress-induced velocity changes. The onset of damage can be predicted by comparing these shallow measurements to a deep velocity measurement in undamaged rock. When the maximum shallow velocity is decreased by damage and approaches the deep velocity, I infer that damage has occurred and breakouts and/or borehole failure are imminent. If implemented in the oilfield, this technique could form the basis for a real-time damage warning for drillers that allows for preventive action.