We present the development of the End-to-End simulator for the SOXS instrument at the ESO-NTT 3.5-m telescope. SOXS will be a spectroscopic facility, made by two arms high efficiency spectrographs, able to cover the spectral range 350-2000 nm with resolving power R˜4500. The E2E model allows to simulate the propagation of photons starting from the scientific target of interest up to the detectors. The outputs of the simulator are synthetic frames, which will be mainly exploited for optimizing the pipeline development and possibly assisting for proper alignment and integration phases in laboratory and at the telescope. In this paper, we will detail the architecture of the simulator and the computational model, which are strongly characterized by modularity and flexibility. Synthetic spectral formats, related to different seeing and observing conditions, and calibration frames to be ingested by the pipeline are also presented.