Predicting the Q–s settlement characteristics of piles is an important element in the designing of pile foundations. The most reliable method in evaluating pile-soil interaction is the static load test, preferably performed with instrumentation for measuring shaft and pile base resistances. This, however, is a mostly post-implementation test. In the design phase, prediction methods are needed, in which numerical simulations play an increasingly popular role. This article proposes a procedure for numerically modeling the interaction of screw displacement piles with soil using the ZSoil 2D FEM program. The procedure takes into account technological characteristics of this type of pile, such as the process of soil expansion during the screwing-in of the auger and the pressure of concrete mix after pile concreting. They significantly affect the soil stress state, which is a key parameter for the pile load capacity. Geotechnical parameters of the subsoil were adopted from CPTU probing and laboratory tests. Due to the physical complexity, a constitutive soil model “Hardening Soil” (HS) was used in the analyses. The modeling procedure was calibrated on the basis of the static load test results of several instrumented piles, which were carried out as part of the “DPDT-Auger” research project. As a result of these calibrations, generalized recommendations were derived for an entire single pile modeling process with the axisymmetric system of ZSoil program. These can be useful in the reliable FEM prediction of the Q–s characteristics for screw displacement piles for practical engineering purposes.