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In this work, a 2D discrete model (DM) applied to the dynamic crack propagation in brittle materials is developed and implemented. The proposed model is based on a particular discretization of Navier's equations, presenting similarities to the Born model, with the advantage that the constants appearing in it are explicitly related to the elastic properties. This model overcomes the limitations in the choice of Poisson's ratio present in other discrete models. Three numerical examples are presented to show the capability of this method in modelling wave propagation and dynamic fracture problems. The obtained results are in agreement with experimental and numerical results reported by other researchers.