The study of crack initiation and propagation is important for the understanding of rock mass behavior, which affects many rock engineering problems. Such studies can be done experimentally in the laboratory or in the field, or numerically. Here, a numerical study is presented, in which the stress and strain fields around a flaw tip were analyzed using the finite element code, ABAQUS, to better understand the processes involved in crack initiation and propagation. Double-flaw geometries were modeled with ABAQUS with the intent of identifying the differences between stress and strain fields around the flaw tip, relating the stress and strain fields to crack initiation and propagation, and comparing numerical results with those of tests performed on gypsum and marble specimens. Both stepped and coplanar flaw geometries were studied, as well as different stages of crack propagation were modeled based upon laboratory results. For the stepped flaws, both stress and strain field analyses correctly explain wing and shear crack initiation and propagation in gypsum and marble. Furthermore, the two analyses are also capable of describing reasonably well tensile and shear coalescence in gypsum and marble, respectively. For the coplanar flaws, it was found that the stress field analysis is capable of explaining wing crack initiation and propagation observed in tests on gypsum and marble. It is also capable of explaining shear coalescence observed in gypsum, but it is not capable of describing the indirect coalescence observed in marble. The strain field analysis is not only capable of satisfactorily explain what the stress field analysis explains, but it also correctly describes the indirect coalescence that occurs in marble specimens.