A numerical model based on the discrete element method (DEM) was developed to study the compaction behaviour of non-spherical particles. Spheroidal and tetrahedral particles of different aspect ratios were approximated by a multi-sphere approach in which overlapping spheres were glued together to represent the particle shapes. For the compactions of spheroidal particles, the effect of aspect ratio on the compaction was mainly due to the difference in the initial packing. The compact compressive strength also increased with the aspect ratio. For the tetrahedral particles, the non-convexity shape index was proposed to represent the degree of inter-particle locking. With increasing non-convexity and thus inter-particle locking, larger consolidation pressure was required to achieve the same density. The failure region upon the unconfined pressure also moved from the bottom to the top with increasing non-convexity as force transfer was more difficult in the compacts. The simulations also indicated that the bulk failure of the compacts was dominated by the shear-induced bond breakage. The findings facilitate a better understanding of the relation of particle shape to the compaction behaviour and compact strength.