The standard bonded-particle models available in many discrete element method (DEM) codes are known to predict unrealistically low values for the ratio of ultimate compressive strength (UCS) to tensile strength (UTS) for concrete. To correct this, various modifications to the bonded particle models or new constitutive laws have been proposed by various researchers. One of these is the Jointed Cohesive Frictional Particle Model (JCFPM) that introduced a parameter called the interaction range to account for high UCS to UTS ratios. In this work, JCFPM model is used to model the response of concrete under uniaxial compressive loading. A parametric study is carried out to study the effect that various DEM parameters such as the cohesion, packing density, particle generation methods and the interaction range have on the response of the concrete cylinder. Based on these studies, a calibrated DEM model that predicts results in agreement with the experimentally observed results is presented.