Despite the massive use of concrete by the construction industry, its optimisation remains a scientific and engineering challenge, that has important implications for the global environ and economy. Difficulties predicting the material behaviour after cracking are part of the problem, since design relies on accurate models. As the cracks start to grow, the hypothesis of material continuity that is critical to the differential equations of the classical theory becomes obsolete. In fact, many issues are documented in the literature regarding the employment of the classical continuum solid mechanics and the finite element method in this context. In order to avoid these problems, the recent peridynamics theory [1] was formulated without differential equations or continuity requirement. This contribution describes a numerical method to solve the peridynamics equations using a simple explicit scheme based on the Euler method [2], where the spatial discretisation consists of a finite set of material particles and interparticle bonds. Cracks may develop by disruption of these interparticle bonds. The onset and evolution of discrete cracks in tensile zones is predicted in this paper using simple examples. The formulation of the method, comparison with the elastic theory and derivation of relations between model parameters and macroscopic elastic modulus are presented. Furthermore, an initial investigation of the model’s ability to reproduce damage through the spontaneous formation of cracks during loading is analysed. The obtained results, may improve the models used to describe concrete structures and materials vulnerable to cracking. Those improved models, may lead to higher construction quality and mitigation of environmental issues.