Abstract: The downstream detonation initiation induced by interaction between the shock wave and the single rectangle obstacle interaction was simulated numerically. The upstream detonation forming and its following wave dynamics which initiated the downstream detonation waves were investigated. From the numerical results two initiation modes, which were the direct detonation diffraction and the diffraction wave reflection on the upper wall, were found out and validated by the previous experimental results. The processes of the upstream detonation transmitting downstream were analyzed by studying the influences of the incident shock Mach number, gas mixture pressure, and the tube length scale. The operating rules and governing factors of two initiation modes were concluded and the downstream detonation initiation rules were illustrated.