We compare the glacial isostatic adjustment (GIA) behaviour of two approaches developed to model the movement of a glacially induced fault (GIF) as a consequence of stress changes in the Earth's crust caused by the GIA process. GIFs were most likely, but not exclusively reactivated at the end of the last glaciation. Their modelling is complicated as the GIA process involves different spatial and temporal scales and they have to be combined to describe the fault reactivation process accurately. Model approaches have been introduced by Hetzel & Hampel (2005, termed HA in this paper) and Steffen et al. (2014a, termed WU in this paper). These two approaches differ in their geometry, their boundary conditions and the implementation of stress changes. While the WU model is based on GIA models and thus includes the whole mantle down to the core-mantle boundary at a depth of 2891 km, the HA models include only the lithosphere (mostly 100 km) and simulate the mantle using dashpots. They further apply elastic foundations and a lithostatic pressure at the base of the lithosphere, while the WU models apply elastic foundations at all horizontal boundaries in the model with density contrasts. Using a synthetic ice model as well as the Fennoscandian Ice Sheet, we find large discrepancies in modelled displacement, velocity and stress between these approaches. The HA model has difficulties in explaining relative sea level curves in Fennoscandia such as the one of Ångermanland (Sweden), where differences of up to 118 m to the data (with data error of 18.7 m) result. The WU model differs by up to 11 m, but falls within the error bar of 11.6 m. In addition, the HA model cannot predict the typical velocity field pattern in Fennoscandia. As we also find prominent differences in stress, we conclude that the simulation of the mantle using dashpots is not recommended for modelling the GIA process. The earth model should consist of both lithosphere and mantle, in order to correctly model the displacement and stress changes during GIA. We emphasize that a thorough modelling of the GIA process is a prerequisite before conclusions on understanding GIF evolution can be drawn.