Edge chipping by an indenter has been used to investigate the fragmentation of brittle materials. This paper proposed a constitutive model for studying both the initiation and propagation of cracks during the chipping of concrete. The analysis was carried out by the finite element method using a commercially available code, LS-DYNA. The results showed that a zone with very high compressive stresses appears beneath the indenter and causes the material to break or crush. Most of the external work, about 78%, was dissipated in the crushing zone while only a small percentage (less than 17%) contributed to form chips/fragments. As the indentation proceeded, radian-median cracks initiated and propagated downward and parallel to the front surface of the material to form a half penny crack. The crack tips from both sides of the indenter on the surface would then deviate toward the free edge, leading to a chipping scallop at a critical load.