Over the years, many attempts have been made to simulate the cone penetration process in coarse-grained and fine-grained soils. The simulation methods range from pure analytical methods to complicated numerical approaches. Among the analytical methods, cavity expansion analysis has gained more attractions due to its relative simplicity and robust theoretical background. Analytical cavity expansion analysis is limited to rather simplistic soil constitutive models. As a result, numerical cavity expansion analyses have been attempted to cover this limitation. Another method that has gained much attention in the past decade is the Material Point Method (MPM) whose promising capabilities in simulating large deformation problems can be used for simulating the cone penetration. In this paper, we model the cone penetration in loose, medium dense and dense sands using numerical spherical cavity expansion method and axisymmetric MPM. In all the analyses, soil behavior is modelled using Mohr-Coulomb constitutive model. The soil is assumed to be dry in all analyses. Results are compared with a cylindrical cavity expansion solution.