Double-Sided Incremental Forming (DSIF) is a rapid-prototyping manufacturing process for metal forming that, for low-volume production, is competitively energy-efficient. However, controlling the DSIF process in terms of accuracy and formability is an ongoing challenge. These control challenges arise due to a lack of understanding of the underlying deformation mechanisms in DSIF, which finite element simulations can help to unravel. However, DSIF pushes the limits of modern finite element formulations due to true strains that approach one, finite rotations, nonlinear contact, and triaxial stress states that range across multiple length scales. To confidently develop a finite element model of DSIF, an extensive verification process must be considered, which is the objective of this study. In this work, different finite element types and varying amounts of artificial acceleration are investigated, and recommendations based on efficiency and accuracy are summarized. A simplified, axisymmetric geometry was considered to reduce simulation time. For this geometry, accelerating the explicit finite element simulation by a mass factor of 105 or greater affected the stress triaxiality in the sheet by as much as 40% in some locations with respect to the quasi-static case. Additionally, the ratio of the kinetic energy to internal energy of the sheet was not a reliable indicator of whether a DSIF simulation is approximately quasi-static.