The paper presents the modelling of the cone penetration test using two procedures: a discrete approach and a continuum approach. The discrete approach is based on the Discrete Element Method where a granular material is represented by an assembly of separate particles. Cone penetration has been simulated for both uncrushable and crushable sands. For the continuum approach, the Particle Finite Element Method has been adapted in order to overcome the difficulties posed by the occurrence of large displacements as well as by the geometrical, material and contact nonlinearities of the problem. Both single phase and two-phase (coupled hydromechanical) formulations have been developed and applied. Although not exempt of problems, both approaches yield realistic results leading to the possibility of a closer examination and an enhanced understanding of the mechanisms underlying cone penetration.