Since the early 1980s, numerical simulations of pile drivability have used rudimentary linear elastic, perfectly plastic soil models, with an added velocity-dependent term. These models are manageable because they are common and have only a small number of parameters: two for the elastoplastic part and one for the damping. However, they render a crude depiction of the soil behavior. A soil model closer to reality could allow for a better prediction and therefore lead to an increased confidence in the simulation results. Unfortunately, attempts to employ more elaborate models are seldom, mainly because the number of soil parameters increases with the complexity of the model. As such, a large set of soil parameters acts as a barrier to entry. This paper highlights the relative importance of the individual soil parameters of such an elaborate critical-state soil model in a pile-driving numerical simulation. The soil model used in the analysis is hypoplasticity for clay coupled to intergranular strain, which has ten parameters that can be readily determined from laboratory tests. The main conclusion of the sensitivity analysis is that only a few soil parameters control the behavior of the soil during driving and subsequent consolidation.