The simulation of penetration problems in geomaterials is a challenging problem as it involves large deformations and displacements as well as strong non-linearities affecting material behaviour, geometry and contact surfaces. The paper presents examples of 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 successfully simulated for the case of crushable sands. For the continuum approach, the Particle Finite Element Method has been adopted. The procedure has been effectively applied to the modeling of undrained cone penetration into clays. 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 penetration problems in geomechanics.