This paper describes a novel method for representing arbitrary grain shapes in discrete element method (DEM) simulations. The method takes advantage of the efficient sphere contact treatment in DEM and approximates the overall grain shape by combining a number of overlapping spheres. The method is based on the medial axis transformation, which defines the set of spheres needed for total grain reconstruction. This number of spheres is then further diminished by selecting only a subset of reconstructing spheres and opting for a grain approximation rather than a full grain reconstruction. The effects of the grain approximating parameters on the key geometrical features of the grains and the overall mechanical response of the granular medium are monitored by an extensive sensitivity analysis. The results of DEM quasi-static oedometric compression on a granular sample of approximated grains exhibit a high level of accuracy even for a small number of spheres.