The accidents that hydrogen ignites without ignition source are reported in several cases, which phenomenon is called 'auto-ignition'. Since the use of high pressure hydrogen will be increased for the hydrogen society, it must be necessary to understand auto-ignition mechanism in detail to prevent such accidents. In this study we performed three-dimensional numerical simulations to clarify the auto- ignition mechanism using the three-dimensional compressive Navier-Stokes equations and a hydrogen chemical reaction model including nine species and twenty elementary reactions. We focus on the effects of the shape of the cross-section on the hydrogen auto-ignition mechanism applying for a rectangular and cylindrical tube. The results obtained indicate that the Richtmyer-Meshukov instability involves these auto-ignition.