Increasing projected values of the circulating beam intensity in the Super Proton Synchrotron (SPS) and decreasing limits to radiation exposure, taken with the increasing non-acceptance of unjustified and unoptimised radiation exposures, have led to the need to re-assess the shielding between the ECX and ECA5 underground experimental areas of the SPS. Twenty years ago, these experimental areas at SPS-Point 5 housed the UA1 experiment, where Carlo Rubbia and his team verified the existence of W and Z bosons. The study reported here describes such a re-assessment based on simulations using the multi-purpose FLUKA radiation transport code. This study concludes that while the main shield which is made of concrete blocks and is 4.8 m thick satisfactorily meets the current design limits even at the highest intensities presently planned for the SPS, dose rates calculated for liaison areas on both sides of the main shield significantly exceed the design limits. Possible ways of improving the shielding situation are discussed.