Aggregates are the major component of asphalt mixtures, so their properties and the way they are packed play a significant role on the mix performance. A two-step research procedure was developed to understand how the packing characteristics of the aggregate particles in an asphalt mixture can be affected by grain shape and size distribution. In the first step, presented in this paper, the combined effect of grain shape and angularity on the packing and stability of an aggregate assembly was investigated using a 3D discrete element method (DEM). The second stage, which will be presented in a later paper, provides a model that, including the effect of binder, can successfully simulate the packing characteristics of asphalt mixtures, and contribute to the improvement of their mix design. The results obtained from several triaxial tests, carried out on different grain-type specimens, show that the particles' shape and angularity significantly affect the behavior of the assembly.