This paper describes SSSim, the Simple and Scalable Simulator for P2P streaming systems. SSSim is designed for performance and scalability, and allows the simulation of the diffusion of a very large number of chunks over large number of peers in reasonable times. This result has been obtained by optimising the simulator for recurrent workloads and minimizing the memory footprint. After describing the simulator's structure and the most important design decisions, the paper presents some experimental results comparing the simulation times of SSSim and a traditional simulator.