Cone Penetration Testing (CPT) is a widely used in situ soil testing technique which allows to estimate soil stratigraphy and various soil parameters. Depending on the soil's consolidation coefficient, undrained, partially drained or drained conditions might occur. Partially drained conditions are commonly encountered in soils such as silt and sand-clay mixtures. Correlations between CPT measurements and soil properties are usually only valid for fully drained or fully undrained conditions which may lead to inaccurate estimates of the properties of silty soils. This paper aims at improving the understanding of the penetration process in different drainage conditions through advanced numerical analyses. A two-phase Material Point Method is applied to simulate the large soil deformations and the generation and dissipation of excess pore pressures that occur during penetration. The constitutive behavior of the soil is modelled with the Modified Cam Clay model. The implemented MPM formulation is validated by comparing numerical results with the results of centrifuge tests under different drainage conditions.