A two-dimensional simulation of concrete behaviour using the discrete element method (DEM) is presented in this work. The main aim of this paper is the modelling of the failure process and crack initiation. The failure process of a concrete prism during a compression test is simulated. A substructure representing the concrete components - aggregate and cement matrix - is introduced. It is shown that convex and concave concrete specimens can be treated, whereas the particle geometry always remains convex. The crack patterns of the concrete specimens resulting from the simulation are shown and compared with laboratory experiments. It is shown that the calculated peak load does not depend on the particle number used in the simulation. The ratio of lateral strain to longitudinal strain of the concrete specimen during load application is simulated and compared with experimental results.