  The Search for Hidden Particles (SHiP) Collaboration has shown that the CERN
SPS accelerator with its 400 $\mathrm{\small GeV/c}$ proton beam offers a
unique opportunity to explore the Hidden Sector. The proposed experiment is an
intensity frontier experiment which is capable of searching for hidden
particles through both visible decays and through scattering signatures from
recoil of electrons or nuclei. The high-intensity experimental facility
developed by the SHiP collaboration is based on a number of key features and
developments which provide the possibility of probing a large part of the
parameter space for a wide range of models with light long-lived superweakly
interacting particles with masses up to O(10) $\mathrm{\small GeV/c^2}$ in an
environment of extremely clean background conditions. This paper describes the
proposal for the experimental facility together with the most important
feasibility studies. The paper focuses on the challenging new ideas behind the
beam extraction and beam delivery, the proton beam dump, and the suppression of
beam-induced background.
