The problem of long-lived radioactive waste has yet to find an acceptable solution, with political opposition to geological storage remaining strong. One possible solution which has often been discussed is to use ADSR systems for its incineration. The advantages of thorium as a fuel in this process are obvious, but few detailed numerical studies have been performed. We investigate the potential for using a thorium fuelled subcritical reactor for the incineration of long-lived minor actinide radioactive waste, based on the well developed MYRRHA reactor design, operating in sub-critical mode. We examine the neutron fluxes and spectra in the reactor, particularly in the In-Pile Section (IPS) regions that would be appropriate for such transmutation, comparing the result from thorium fuel rods with those of the standard uranium/plutonium fuel. From this we present the burn-up rates that would be achieved, both initially and in the longer term as U-233 is formed. Copyright (C) 2016, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.