The planned Multipurpose Hybrid Research Reactor for High-Tech Applications (or MYRRHA) research reactor in Mol, Belgium, aims to demonstrate efficient transmutation of high-level waste and associated accelerator-driven systems technology. The system is based on a lead-bismuth eutectic cooled reactor, working both in critical and in subcritical operation modes. The neutrons needed to sustain fission in the subcritical mode are produced via spallation processes by a 600-MeV less than or equal to 4 mA proton beam, which is provided by a linear accelerator and hits a lead-bismuth eutectic spallation target located inside the reactor core. In order to assess the main shielding problems, a method based on the combined use of the two Monte Carlo codes MCNP and FLUKA was developed, with the goal to perform detailed analyses of both the radiation fields due to the system in operation and the coupled residual radiation due to the activated materials. As a result, neutron and photon fluences as well as prompt and residual ambient dose equivalent rates were evaluated. In addition, an activation database for many of the structural materials was built.