A stochastic rock fissure hazard model is presented based on geological characterization of the occurrence and propagation of fissures. The hazard model is developed in two steps: (1) fissure propagation model and (2) fissure occurrence model. For the fissure propagation model, the initiation point, length, azimuth and depth of fissures are described as random variables that define the spatial distribution, direction and extent of fissure propagation in a specified volume. From the model probabilities of a fissure crossing an underground waste repository can be estimated given that a fissure has been initiated. Fissure occurrences are represented as a Poisson stochastic process. The fissure occurrence and fissure propagation models are combined to obtain the probability of fissures crossing a waste repository as a function of time. In particular, probabilities of at least one fissure crossing the repository at a site during the life of a repository can be estimated with the proposed model.