In this paper we present a complete and detailed computational model of the response of the hybrid Muon Telescope (MuTe), designed to perform muography volcanic studies. This instrument combines two particle detection techniques: first, a muon hodoscope based on two panels of plastic scintillator bars; and a Water Cherenkov detector located behind the rear scintillator panel acting both as a coincidence and a discriminating detector. The simulation model includes: materials, geometries, dimensions, and the photo-sensitiveness of the detectors. The simulation results, in agreement with the measured data, were used to set up the muon detector trigger for the expected energy dependent signal.