Neutronics calculations have been performed of the MYRRHA ADS Reactor with a thorium-based fuel mixture, using the simulation programs MCNPX (Waters, 2002) and Geant4 (Agostinelli, 2003). Thorium is often considered for ADS systems, and this is the first evaluation of the possibilities for thorium based fuels using a reactor design which has been developed in detail. It also extends the application of the widely-used Geant4 program to the geometry of MYRRHA and to thorium. An asymptotic 232Th/233U mixture is considered, together with the standard MOX fuel and a possible 232Th/MOX starter. Neutron fluxes and spectra are calculated at several regions in the core: fuel cells, IPS cells and the two (Mo and Ac) isotope production cells. These are then used for simple calculations of the fuel evolution and of the potential for the incineration of minor actinide waste. Results from the two programs agree and support each other and show that the thorium fuel is viable, and has good evolution/breeding properties, and that minor actinide incineration, though it will not take place on a significant scale, will be demonstrable.