We present the progresses of the simulation tools, the Exposure Time Calculator (ETC) and End-to-End simulator (E2E), for the Son Of X-Shooter (SOXS) instrument at the ESO-NTT 3.58-m telescope. The SOXS will be a single object spectroscopic facility, made by a two-arms high-efficiency spectrograph, able to cover the spectral range 350-2000 nm with a mean resolving power R approximate to 4500. While the purpose of the ETC is the estimate, to the best possible accuracy, of the Signal-to-Noise ratio (SNR), the E2E model allows us to simulate the propagation of photons, starting from the scientific target of interest, up to the detectors. We detail the ETC and E2E architectures, computational models and functionalities. The interface of the E2E with external simulation modules and with the pipeline are described, too. Synthetic spectral formats, related to different seeing and observing conditions, and calibration frames to be ingested by the pipeline are also presented.