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The NASA InSight mission will provide an opportunity for soil investigations using the penetration data of the heat flow probe built by the German Aerospace Center DLR. The Heat flow and Physical Properties Probe (HP^3) will penetrate 3 to 5 meter into the Martian subsurface to investigate the planetary heat flow. The measurement of the penetration rate during the insertion of the HP3 will be used to determine the physical properties of the soil at the landing site. For this purpose, numerical simulations of the penetration process were performed to get a better understanding of the soil properties influencing the penetration performance of HP^3. A pile driving model has been developed considering all masses of the hammering mechanism of HP^3. By cumulative application of individual stroke cycles it is now able to describe the penetration of the Mole into the Martian soil as a function of time, assuming that the soil parameters of the material through which it penetrates are known. We are using calibrated materials similar to those expected to be encountered by the InSight/HP^3 Mole when it will be operated on the surface of Mars after the landing of the InSight spacecraft. We consider various possible scenarios, among them a more or less homogeneous material down to a depth of 3–5 m as well as a layered ground, consisting of layers with different soil parameters. Finally we describe some experimental tests performed with the latest prototype of the InSight Mole at DLR Bremen and compare the measured penetration performance in sand with our modeling results. Furthermore, results from a 3D DEM simulation are presented to get a better understanding of the soil response.