CERN is at present designing a new chain of accelerators to replace the present Proton Synchrotron (PS) complex: a 160-MeV room-temperature linear accelerator (linac) (Linac4) to replace the present 50-MeV linac injector, a 3.5-GeV superconducting proton linac (SPL) to replace the 1.4-GeV PS booster, and a 50-GeV synchrotron to replace the 26-GeV PS. Linac4 has been funded, and civil engineering will start soon, while the SPL is in an advanced stage of design. Beyond injecting into the future 50-GeV PS, the ultimate goal of the SPL is to generate a 4-MW beam to produce intense neutrino beams. The radiation protection design is driven by the latter requirement. This work summarizes the radiation protection studies conducted so far for Linac4. The calculations of the shielding, access maze, ducts for cables, waveguides, and ventilations were performed with the FLUKA Monte Carlo code, complemented by analytical estimates.