A simple fracture mechanics approach is used to predict the critical crack size required to initiate Hertzian cracks in a brittle material in the absence and presence of a residual surface stress. To test the approach, the load and location of ring/cone cracks are measured in a silicate glass before and after ion exchange. The crack sizes estimated by this technique are, however, different before and after the ion-exchange process. It is concluded that the ion-exchange process changes the nature of the surface flaws, which is a key assumption in previous theoretical analyses in using Hertzian contacts as a means to estimate surface stress.