Of the various methods for measuring the fracture energy of a material, the three-point slow bend test has the merit of being simple and straightforward to execute. It can only be expected to give valid results, however, when the crack propagates quasi-statically. A simple criterion is proposed to determine whether a specimen of given geometry and meterial will fracture in a stable or unstable manner when tested in a particular machine. The prediction of the criterion is compared with experimental results obtained on a variety of rocks, and is found to give good agreement.