The experiments of high-velocity flyer acceleration were performed on the HEAVEN-I KrF laser facility with a long-pulse duration (∼ 28 ns). Double-layered flyers consisting of polystyrene and aluminum films can be accelerated to more than 10 km/s measured by VISAR. The polystyrene layer is used as the ablative material, insulation layer, and shock wave regulator. Multiple shock and acceleration processes were observed by adjusting the thickness of the polystyrene layer. We simulated and analyzed the multiple shock processes driven by the long laser pulses and square pressure pulses. The results indicate that the reverberation processes can be induced by the alternating shock and rarefaction waves due to the wave–interface interactions. The reverberations in the Al layer can modulate the pressure evolution and the fine structure of flyer acceleration history. Similar processes in the polystyrene layer can lead to a secondary or multiple shock loading process when the driving pulse duration is several times longer than the shock round trip time in the double-layered flyer. Multiple accelerations can effectively enhance the final velocities in the experimental and simulation results. However, multiple accelerations involve more complex shock loading and unloading processes, and flyers are more prone to breakup compared with single acceleration.