The critical load for cone crack initiation in a brittle material indented by a rigid cylindrical punch is related to the fracture toughness of the material and the punch radius through the classical energy principles. The strain energy required to form an embryo cone crack on a flaw-free surface adjacent to the punch edge is formulated, from which the critical load for cone cracking is then determined. The present analysis shows that the stress singularity close to the sharp contact edge is akin to that a sharp crack tip. The results in this study can be used to set up a simple and practical technique for evaluating some strength-related properties of brittle materials such as the fracture toughness.