The feasibility of a Beam Dump Facility (BDF) is presently being studied at CERN. Beam dump in this context implies a target aimed at absorbing all incident protons and containing most of the cascade generated by the primary beam interaction. The proposal is a general-purpose fixed target facility to be situated at the North Area experimental zone of the Super Proton Synchrotron (SPS). In the initial phase, the facility would serve a general Search for Hidden Particles (SHiP) experiment as part of the search for new physics beyond the Standard Model. Feasibility studies are ongoing at CERN to address the key challenges of the facility. The supercycle-averaged power of the 400 GeV primary proton beam will be around 355 kW, while the beam energy is in the order of 2.6 MJ/pulse. The associated high prompt and residual dose rates call for considerable shielding and remote interventions in the target area. Potential radiological risks to personnel and environment from air, water and soil activation heavily influence the design. In order to respect the applicable CERN radiation protection legislation regarding doses to personnel, a preliminary radiological study was carried out. To assess the above-mentioned radiation protection aspects, extensive simulations were performed with the FLUKA Monte Carlo particle transport code. This paper will describe the concept of the facility and will summarize first assessments related to radiation protection.