The GLAST Burst Monitor (GBM) is designed to provide wide field of view observations of gamma-ray bursts and other fast transient sources in the energy range 10 keV to 30 MeV. The GBM is composed of several unshielded and uncollimated scintillation detectors (twelve NaI and two BGO) that are widely dispersed about the GLAST spacecraft. As a result, reconstructing source locations, energy spectra, and temporal properties from GBM data requires detailed knowledge of the detectors' response to both direct radiation as well as that scattered from the spacecraft and Earth's atmosphere. This full GBM instrument response will be captured in the form of a response function database that is derived from computer modeling and simulation. The simulation system is based on the GEANT4 Monte Carlo radiation transport simulation toolset, and is being extensively validated against calibrated experimental GBM data. We discuss the architecture of the GBM simulation and modeling system and describe how its products will be used for analysis of observed GBM data. Companion papers describe the status of validating the system.