Granular materials, of which sand is the most prominent representative, are important in many fields of research. Their special properties make them important both for industrial applications and as a field of work in basic research. The present work deals with the numerical investigation of granular materials. The size scale of typical granular particles starts in the micrometre range for fine dusts. The upper limit is approximately in the range of a few kilometres particle diameter for the boulders in the rings of Saturn. Although one generally thinks of large numbers of particles in granules, this is not necessary to obtain interesting systems. Even studying the dynamics of a single particle in contact with a wall can yield interesting insights. A few dozen marbles in a Petri dish already show novel behaviours such as the so-called reptation motion. To investigate more complex systems with the help of a computer simulation, it is necessary to be able to calculate sufficiently large numbers of particles. In this case, it makes sense to make better use of the available computing time by implementing optimised algorithms. The shape of the particles in a granular medium is also of particular importance. Round, smooth dragées in a pharmaceutical company certainly have different properties than the rough ore lumps in mining. For this reason, the shape of the particles was also taken into account in the simulation programme created for this work. An even more complicated behaviour can arise if granulates still interact with liquids or gases. Likewise, the shape of the interaction between two particles has an influence on the behaviour of the overall system. If another attractive force is added to the force due to collisions, the influence of cohesion can be investigated. The thesis is structured as follows: first, in chapter 1, those basic properties of granulates are discussed that are of importance for the systems investigated. In the following chapter 2, the simulation methods used are presented and explained. This includes the physical modelling of the contacts, the evaluation of the simulation results, the test of the numerics and the strategies used to perform the simulation in an acceptable time. The following two sections then deal with the investigation of two different systems. Chapter 3 deals with bulk columns; here an extension of Janssen's classical theory is presented and compared with simulations. Chapter 4 then describes simulation results that provide insight into sand heaps. Quantities of interest to the theories are examined. Likewise, an attempt is made to direct the view to a quantity that has not been considered so far, the local density. Finally, the results of the work are summarised again and evaluated with regard to future developments.