The CALICE Semi-Digital Hadronic Calorimeter technological prototype is a sampling calorimeter using Glass Resistive Plate Chamber detectors with a three-threshold readout as the active medium. This technology is one of the two options proposed for the hadronic calorimeter of the International Large Detector for the International Linear Collider. The prototype was exposed to beams of muons, electrons and pions of different energies at the CERN Super Proton Synchrotron. To be able to study the performance of such a calorimeter in future experiments it is important to ensure reliable simulation of its response. This paper presents the SDHCAL prototype simulation performed with GEANT4 and the digitization procedure achieved with an algorithm called SimDigital. A detailed description of this algorithm is given and the methods to determinate its parameters using muon tracks and electromagnetic showers are explained. The comparison with hadronic shower data shows a good agreement up to 50 GeV. Discrepancies are observed at higher energies. The reasons for these differences are investigated.