The Edinburgh model (Brown et al. in Granular Matter 16:299–311, [1]) as an addition of the discrete element method allows to define a tool to simulate cohesive granular materials due to its capacity to represent, in case of concrete, the coarse aggregate as particles and the cementitious matrix as bond between elements. The Edinburgh Bonded Particle Model (EBPM) defines its operation through two different contact models, the theory of the Timoshenko Beam Bonded Model (TBBM) when particles are bonded, and the Hertz-Mindlin Contact Model (HMCM) when the connection between elements is broken. The purpose of this work is to computationally represent different structures of civil engineering (Molina, Tavarez and Plesha in Int J Numer Meth Eng 70:379–404, [2]) through the Edinburgh Bonded Particle Model and analyze their behavior. These models represent basic civil engineer structures with the purpose of comparing their behavior with real documented results. Two classical models are studied, a dam with distributed hydrostatic force at three different water levels and a cantilever beam with the application of a dynamic force. The result of the simulation is the behavior of two concrete structures, and through different parameters like forces, displacement of the particles and their bonds is possible to represent the deformation and cracking of the material by analyze the results in different timesteps. This method is capable of adequately represent the elastic and inelastic behavior of concrete during loading process, and its open a gap to continuing researching about the method and its applications in civil engineering.