Concrete is regarded as a skeleton of aggregate particles of various sizes, almost in direct contact with each other. The cement matrix acts as a filler and adhesive enabling the structure to be able to carry tensile stresses. A 2D circular rigid discrete element formulation based on the Discrete Element Method has been adopted. Random assemblies of particles based on a given sieve analysis can be generated enabling the simulation of the concrete structure at the meso-level. Contact models that are able to transmit moments through the contact plane have been implemented, namely, a developed contact model adopting more than one contact point at the contact plane. The steel reinforcement has been modelled with 1D beam finite elements or with 1D rigid discrete elements that interact with the discrete rigid particles through contact interfaces. Softening has been introduced into the microlevel constitutive equations. The traditional DEM has been enhanced with a boundary wall driven by force algorithm, an adaptive global damping algorithm and an arc-length control algorithm increasing the range of applicability and the performance of the model. The behavior of a double notched plain concrete specimen is investigated. Comparison of results in terms of crack patterns and load displacement relationships up to the peak load with both experimental and numerical results obtained using a lattice beam element formulation showed good agreement. The performance of the developed DEM model has also been evaluated for uniaxial tension, uniaxial compression and tensile splitting tests. The developed model showed good agreement in terms of peak strength, fracture localization and crack patterns. Finally the interaction between the stiffness of the reinforcement normal to the plane of cracking and the shear stiffness due to aggregate interlock is investigated. Good comparisons in terms of shear force and shear displacement relationships for a given crack width and reinforcement stiffness were obtained with known experimental data