Fast ice (FI) refers to sea ice that remains mechanically immobilised along the coast for extended periods. In the Arctic, its presence influences the stability of the halocline by displacing polynyas offshore and by altering the mixing of river plumes. In numerical ocean-sea-ice models, the realism of simulated FI depends on how grounding processes and sea ice rheology are accounted for. Indeed, grounding parameterisations define if, where, when and how anchor points establish in shallow seas, whereas sea ice rheology dictates the way sea ice dynamics respond to the mechanical forcings. Here, we assess the direct impact of the rheological formulation on the simulation of Arctic FI, as well as its indirect effect when an additional grounding scheme is included. Using the Nucleus for European Modelling of the Ocean – Sea Ice modelling Integrated Initiative (NEMO-SI³) on a 0.25° global grid, we conduct experiments using two different rheological frameworks—the adaptive Elastic-Viscous-Plastic with tensile strength (aEVPts) and the brittle Bingham-Maxwell (BBM), each tested with and without a state-of-the-art grounding scheme. The results show the primary importance of the grounding scheme to simulate Arctic FI. We also find that grounding and rheology interact: BBM produces more rigid sea ice than aEVPts, which favors the formation of FI, but also ridges less easily, which inhibits grounding, and ultimately reduces FI coverage. Comparison with in situ thickness measurements further highlights the importance of accurate timing and duration of immobilisation: when ice is locked early and primarily grows through thermodynamic processes, modelled thickness errors are significantly reduced.