Abstract: The near-axisymmetric contraction flow in internal cones with different angles of attack is proposed to simplify the complicated three-dimensional shock interactions in a hypersonic inward-turning inlet. The interactions of the shock at near-axisymmetric contraction conditions are revealed efficiently using a combination of experiments in a shock tunnel and numerical simulations. The results show that the axisymmetric incident shock strengthens toward the central axis due to the convergence effect until a Mach disk is formed. It has been shown that the Mach reflection at the central axis is an inevitable phenomenon, which prevents the convergence and enhancement of the axisymmetric incident shock even for a small compression angle of the leading edge of the internal cone. However, when the incoming flow has an angle of attack, the flow field deviates slightly from the axisymmetric state and presents complex three-dimensional characteristics. The windward incident shock strengthens faster than the leeward incident shock along the flow direction. As a result, the shock interaction position on the symmetry plane deviates from the axis and the regular reflection can occur. The local pressure immediately downstream the reflection position for the regular reflection can reach a much higher level than that behind the Mach disk for the conditions where the Mach reflection occurs. Moreover, with the increase of the leading edge compression angle of the internal cone, the critical angle of attack for the appearance of the regular reflection on the symmetry plane also increases.