Hypersonic Inflatable Aerodynamic Decelerator (HIAD) has shown its great potential for future planetary explorations. However, the HIAD surface deflections could both promote boundary-layer transition early and augment heating levels sharply, which poses challenges for survivability of a Thermal Protection System (TPS). The goal of this work is to assess different transition models for the prediction of hypersonic transitional flows over scalloping deformed HIAD surface and to seek the critical factor for their capabilities to provide a reference for the application and advancement. Three representative transition models are considered: gamma-Re-theta, k-omega-gamma and k(T)-k(L)-omega. The results show that the undulating surface causes flow separations and reattachments in valleys and strong crossflow along the leeward. k-omega-gamma model can correctly predict both the shapes and locations of the transition onsets. The transition zone predicted by gamma-Re-theta model is much small, while k(T)-k(L)-omega is incapable of transition prediction for such a complex and irregular configuration. Moreover, this study reveals that the crossflow instability plays a dominant role in the transition. The crossflow Reynolds number Red, whose distributions are approximately consistent with the transition zone, could be a feasible crossflow strength indicator for the transition onsets on the undulating surface. Once k-omega-gamma model excludes effects of crossflow instability, it predicts incorrect transition results for the deformed surface of HIAD. Besides, a detailed analysis shows that both the crossflow instability mode and the first disturbance mode in valleys are the major contributors to the transition on the leeward surface. Near the leeward ray, the transition is mainly determined by the first disturbance mode. (C) 2018 Elsevier Ltd. All rights reserved.