The EURopean Isotope Separation On-Line Radioactive Ion Beam (EURISOL) project aims at building a facility to produce radioactive ion beams with intensities two to three orders of magnitude higher than those presently available. A 4-MW (1-GeV, 4-mA) proton beam hits a liquid mercury converter, generating, by spallation reactions, high neutron fluxes that induce fission in surrounding fissile targets. In this work, Monte Carlo calculations of dose rate and activation were carried out to identify the necessary shielding and access restrictions for each section of the facility, including maintenance, storage, and remote control spaces. These calculations allowed an optimization of the materials chosen for the assembly, based on the radioprotection issues, while taking into account the desired performance of the system. The results of the design studies indicate that the intended performance parameters (namely neutron fluxes, fission rates, and easy fission target manipulation) of the EURISOL multimegawatt target station are in reach. The safety analysis indicates that some regions of the facility need special attention from the safety and radioprotection points of view.