A stone cutting process is proposed using the ideas of linear elastic fracture mechanics and a pre-stress concept. A simple mathematical model was devised to study this process and to predict crack take-off angles as well as the convexity of the crack surface. It was found that take-off angles could be regulated by means of varying the beam height and/or the pre-stressing. Numerical results are compared to experimentally obtained data and found to be in good agreement within experimental measurements.