In this work the installation process of a cone penetrating into a sand system is modelled using a 2D-axisymmetric material point method (MPM) model in order to investigate the installation processes and to predict the plastic radius. One meter of cone penetration is modelled under a surcharge of 50 kPa. The used constitutive model is Mohr-Coulomb Strain Softening (MCSS). The validation of the model has been conducted by comparing the MPM results to those obtained from laboratory experiments performed by Arshad et al. (2014). It was found that the qualitative behaviour from the MPM model and the experiments were in agreement but the quantitative behaviour showed some discrepancies. These discrepancies could be caused by the fact that, in the MCSS model, the stiffness is constant and independent of stress which it is not in reality. The performed sensitivity analysis showed that the stiffness has the most influence on the numerical predictions further adding to the importance of accurately capturing the soil stiffness throughout the simulation. The 2D-axisymmetric MPM model showed to have the potential to be a good tool for modelling the installation process of a cone and predicting the plastic radius.