The scientific problems related to granular matter are ubiquitous. It is currently anactive area of research for physicists and earth scientists, with a wide range of applicationswithin the industrial community. Simple analogue experiments exhibit behaviour that isneither predicted nor described by any current theory. The work presented here consistsof modelling granular media using a two-dimensional combined Finite-Discrete ElementMethod (FEM-DEM). While computationally expensive, as well as modelling accuratelythe dynamic interactions between independent and arbitrarily shaped grains, this methodallows for a complete description of the stress state within individual grains during theirtransient motion. After a detailed description of FEM-DEM principles, this computational approach isused to investigate the packing of elliptical particles. The work is aimed at understandingthe influence of the particle shape (the ellipse aspect ratio) on the emergent properties ofthe granular matrix such as the particle coordination number and the packing density. Thediff erences in microstructure of the resultant packing are analysed using pair correlationfunctions, particle orientations and pore size distributions. A comparison between frictionaland frictionless systems is carried out. It shows great diff erences not only in the calculatedporosity and coordination number, but also in terms of structural arrangement and stressdistribution. The results suggest that the particle s shape a ffects the structural order of theparticle assemblage, which itself controls the stress distribution between the pseudo-staticgrains. The study then focuses on describing the stress patterns or \force chains" naturallygenerated in a frictional system. An algorithm based on the analysis of the contactforce network is proposed and applied to various packs in order to identify the forcechains. A statistical analysis of the force chains looking at their orientation, length andproportion of the particles that support the loads is then performed. It is observedthat force chains propagate less efficiently and more heterogeneously through granularsystems made of elliptical particles than through systems of discs and it is proposedthat structural diff erences due to the particle shape lead to a signifi cant reduction in the length of the stress path that propagates across connected particles. Finally, the e ffectof compression on the granular packing, the emergent properties and the contact forcedistribution is examined. Results show that the force network evolves towards a morerandomly distributed system (from an exponential to a Gaussian distribution), and itconfi rms the observations made from simulations using discs. To conclude, the combined finite-discrete element method applied to the study ofgranular systems provides an attractive modelling strategy to improve the knowledge ofgranular matter. This is due to the wide range of static and dynamic problems that can betreated with a rigorous physical basis. The applicability of the method was demonstratedthrough to a variety of problems that involve di fferent physical processes modelled withthe FEM-DEM (internal deformations, fracture, and complex geometry). With the rapidextension of the practical limits of computational models, this work emphasizes theopportunity to move towards a modern generation of computer software to understandthe complexity of the phenomena associated with discontinua.