This paper deals with measured as well as calculated parameters of thermal neutron transport in the reactor pressure vessel model, located behind the LR-0 reactor vessel. A VVER-1000 mock-up core placed in the LR-0 reactor is the source of neutrons, whose transport through heavy steel structures surrounding the core (i.e., the side reflector up to the area behind LR-0 vessel), is studied. The change of neutron distribution due to the variable thickness of the steel reactor pressure vessel (RPV) layers was measured and calculated using MCNPX code. The experimental results are compared with calculations performed with CENDL 3.1 and ENDF/B VII using both the thermal scattering law sublibrary with the model and the free gas transport model. When steel thickness increases, the measured reaction rate attenuation coefficients show a considerable decrease in thermal neutron flux, while measured Cd ratios show a faster decrease in the thermal part of the neutron spectra than the epithermal part. The calculation to experiment (C/E) for the Cd ratio shows in most cases better correspondence when the thermal neutron transport is described by means of a free gas transport model than with the thermal scattering law (TSL) model. Significantly better agreement of reaction rates is observed for the epithermal reaction rate attenuation coefficients than for thermal ones. The results are similar for both the free gas and TSL models at these energies.