The Material Point Method (MPM) has been employed in the study of many geotechnical large deformation problems. This study aims at showing: the effectiveness of MPM in simulating a CPT, and the possibility to calibrate the model input parameters by inverse analysis. The MPM schematization adopted to implement the CPT boundary value problem uses a moving mesh concept to model the cone as a rigid body penetrating into the soil. A gradient-based non-linear regression analysis is used to calibrate the input parameters of the constitutive law adopted to model the soil. To this aim, a synthetic case study has been set up, using the model results of a “base” simulation as observations and, in particular, the cone resistance values computed at 24 different depths. The results of the performed sensitivity, parametric and inverse analyses highlights few important aspects related to the use of optimization algorithms to calibrate the input parameters of MPM models of CPTs.