  The Search for Hidden Particles (SHiP) Collaboration has proposed a
general-purpose experimental facility operating in beam-dump mode at the CERN
SPS accelerator to search for light, feebly interacting particles. The SHiP
experiment incorporates two complementary detectors. The upstream detector is
designed for recoil signatures of light dark matter (LDM) scattering and for
neutrino physics, in particular with tau neutrinos. It consists of a
spectrometer magnet housing a layered detector system with high-density
LDM/neutrino target plates, emulsion-film technology and electronic
high-precision tracking. The downstream detector system aims at measuring
visible decays of feebly interacting particles to both fully reconstructed
final states and to partially reconstructed final states with neutrinos, in a
nearly background-free environment. The detector consists of a 50\m long decay
volume under vacuum followed by a spectrometer and particle identification
system with a rectangular acceptance of 5\,m in width and 10\,m in height.
Using the high-intensity beam of 400\gev protons, the experiment aims at
profiting from the $4\times 10^{19}$ protons per year that are currently
unexploited at the SPS, over a period of 5--10 years. This allows probing dark
photons, dark scalars and pseudo-scalars, and heavy neutral leptons with
GeV-scale masses at sensitivities that largely exceed those of existing and
projected experiments. The sensitivity to light dark matter reaches well below
the dark matter relic density limits in the range from a few \mevcc up to
100\,MeV-scale masses, and it will be possible to study tau neutrino
interactions with unprecedented statistics. This paper describes the SHiP
experiment baseline setup and the detector systems, together with performance
results from prototypes in test beams, as it was prepared for the 2020 Update
of the European Strategy for Particle Physics.
