The CERN Proton-Synchrotron (PS) accelerator is currently equipped with two internal beam dumps in operation since the 1970s. An upgrade is required to be able to withstand the beams that will be produced after the end of the LIU (LHC Injector Upgrade) project. For the design of the new dumps, the interaction and transport of beam and all secondary particles generated has been simulated using FLUKA. The working principle of the PS internal beam dump is peculiar compared to the other beam dumps in the CERN accelerator complex: a moving dump intercepts the circulating beam during fewmilliseconds similarly to a fast scraper. The moving dump shaving the beam, the multi-turn transport of beam particles in the PS accelerator, and a time-dependent energy deposition in the dump were modeled. The methodology used in the FLUKA simulations and the comparison with experimental results are presented.