The numerical modelling of a cone penetration test (CPT) has long been a challenging task due to the large deformations associated with the penetration of a CPT. Recent developments in advanced numerical methods have shown promising results in overcoming these difficulties by using the Material Point Method (MPM). In this thesis it is researched whether the MPM is able to reliably produce CPT results in dry sand by using a state-dependent constitutive model. Calibration chamber (CC) tests are modelled for dry sand and results are compared with experimentally performed CC tests in the laboratory. Features regarding the numerical setup and applied boundary conditions which quantitatively influence modelling results are identified and assessed before the model is validated to real CC test data. Validation results show that the model is able to accurately produce cone resistance values for different types of sand for soil states that can be categorised as moderately-dense to dense. Last, it is shown how parameters within the constitutive framework affect the model output and a quantification of the sensitivity of the parameters to model results is presented.