The present paper investigates the suitability of a Discrete Element Method (DEM) to simulate cracks initiation and propagation in heterogeneous media. We focus our studies on the cohesive hybrid-particulate model in which the continuous medium is modeled using a cohesive beam model. Previous works exhibited the ability of such an approach to simulate the mechanical behavior of continuous materials under various solicitations. The DEM is actually well-suited to take into account local heterogeneities and complex fracture phenomena occurring at very fine scales. In a first step, several tests are perfdrmed in the context of a 2D homogeneous medium in order to better quantify micro-macro scale transition effects related to the DEM on cracks initiation and propagation. Then, in a second step, unidirectional fibre-reinforced composites are modeled using 2D models taking into account a brittle matrix failure and interfacial debonding effects. Numerical tensile tests are set up for two main configurations: a single fiber composite constituted of a single fiber embedded in an alumina matrix and the case of multi-fiber composites constituted of parallel fibers also embedded in an alumina matrix. The results exhibit the suitability of the DEM to yield suitable stress fields and crack patterns in the investigated heterogeheous media. Scale transition effects are noticeable in terms of stress fields but turn out to be relatively limited in the mechanism leading to cracks initiation and propagation. Furthermore, the competition between debonding and failure is also well captured whatever the fiber arrangement. (C) 2016 Elsevier Ltd. All rights reserved.