The compaction of granular materials is a process encountered in a wide variety of systems – both naturally occurring and man-made. It is utilized by many industries from ceramical and metallurgical to the chemical and pharmaceutical ones. In fact, the currently most prevalent device for drug delivery – the solid tablet is produced through the process of powder compaction. A clear understanding of the dependence of the mechanical properties of the solid product on both the characteristics of the starting materials and the system dynamics during the process itself is crucial for the effective design, control and scale-up of powder compaction. For this purpose, a quasicontinuum approach has been implemented to simulate the compaction of confined heterogeneous granular systems consisting of particles of different sizes as well as made up from different materials. Quasicontinuum models rely on a finite element framework, in which the displacement of most constrained particles is computed based on the displacements of the nodes of an adaptive mesh. In this formulation inter-particle forces are resolved locally, while their relative displacement is represented using a constrained field. Equilibrium is enforced weakly using the principle of virtual displacement. This method is particularly well suited for the post-rearrangement stage of compaction, where compaction proceeds mostly through elastic and plastic deformation. It allows the dynamic computation of macroscopic variables, such as pressure and density, as well as the resolution of micro-level quantities, such as coordination number and loading paths.