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Impact penetration into soils is one of the most challenging phenomena to model using numerical techniques due to the very rapid large-deformations and water-soil-structure interaction problems involved in the process. In this work, portable free fall penetration testing (FFP) in dry and saturated sands is modeled using the material point method (MPM). MPM is a powerful tool for large-deformation applications in history-dependent materials. A parametric analysis is performed to understand the influence of the soil stiffness and the water excess pore pressures produced during the impact. The effect of the sand stiffness is studied by modifying its Young’s modulus, and the effect of the water is considered by comparing a fully dry model with a fully coupled hydro-mechanical model. The results indicate that the stiffness of the sand strongly controls the appearance of a general bearing capacity failure, which produces deceleration responses with more than one peak, dissimilar to physical tests. In the case of fully saturated sand, the penetration depth is lower than for dry sand with the same properties and the kinematical response of the FFP is consistent with experiments. The results are promising and encourage further development of the simulations.