Optimisation of performance and reduction of costs of structures are major issues in engineering. However, this optimisation requires very accurate numerical models to predict the behaviour of the structures that are currently not available for concrete structures after they start cracking.Since concrete may develop cracks, which contradict the classical solid mechanics assumption of a continuum, the results obtained are in general not satisfactory. The classical theory of solid mechanics is formulated in terms of differential equations relying on the basic assumption of material continuity that does not exist in the cracked material. The presented model is based on the existing peridynamics theory which describes the mechanics of materials by employing integral equations, which are valid during cracking. The discretization of the structure in a set of material particles, correspondent interactions and an explicit scheme of integration based on Verlet method are described. Cracks can form by the breaking of interparticle bonds. The capacity of the model to predict the development of discrete cracks in tensile zones was verified with simple numerical tests.This work can provide the basis for more accurate strategies of predicting concrete structures and similar materials behaviour. The main consequences would be the reduction environmental impacts, cost of construction and also the development of new architectonic concepts along with developments in other industries.