A complex activity of Monte Carlo simulation has been started by the GRBM hardware team in which the entire SAX satellite is described in a 3D geometrical reconstruction ([Rapisarda et al. 1997]). This code is being used for the simulation of the on-ground calibration set-up, and once a good level of confidence is reached on that, it will be used to reconstruct direction, intensity and spectrum of the cosmic Gamma Ray Bursts. In this section we briefly describe the Monte Carlo set-up, discussing the approach to the work and the approximations that need to be done. Then the first results of the simulations are shown and compared, for some monochromatic energies and for several incoming directions, to the results obtained during the on-ground calibrations.