Observations evidence extremely stable boundary layers (SBL) over the Antarctic Plateau and sharp regime transitions between weakly and very stable conditions. Representing such features is a challenge for climate models. This study assesses the modeling of the dynamics of the boundary layer over the Antarctic Plateau in the LMDZ general circulation model. It uses 1 year simulations with a stretched-grid over Dome C. The model is nudged with reanalyses outside of the Dome C region such as simulations can be directly compared to in situ observations. We underline the critical role of the downward longwave radiation for modeling the surface temperature. LMDZ reasonably represents the near-surface seasonal profiles of wind and temperature but strong temperature inversions are degraded by enhanced turbulent mixing formulations. Unlike ERA-Interim reanalyses, LMDZ reproduces two SBL regimes and the regime transition, with a sudden increase in the near-surface inversion with decreasing wind speed. The sharpness of the transition depends on the stability function used for calculating the surface drag coefficient. Moreover, using a refined vertical grid leads to a better reversed ''S-shaped'' relationship between the inversion and the wind. Sudden warming events associated to synoptic advections of warm and moist air are also well reproduced. Near-surface supersaturation with respect to ice is not allowed in LMDZ but the impact on the SBL structure is moderate. Finally, climate simulations with the free model show that the recommended configuration leads to stronger inversions and winds over the ice-sheet. However, the near-surface wind remains underestimated over the slopes of East-Antarctica.