This work presents the analysis of neutron streaming through a tungsten-based shield, modelled as a set of interconnecting tungsten plates, cooled by an aqueous lithium salt solution. The plates are connected with right-angle bends, and then merge to a stainless-steel casing. Discrete neutron streaming paths exist through the right-angle connections and through the stainless steel joints. The analysis was performed in one and two dimensions, with discrete ordinates codes, and in three dimensions with a Monte Carlo code. The results indicate clear streaming paths, both behind ducts and also in cases were materials with very different neutron mean free paths are connected. The neutron flux was observed to peak behind the stainless-steel joints, when compared to adjoining tungsten shield sections. Streaming through the right-angle connections between tungsten plates was limited. The discrete ordinate codes (with low order quadrature sets), generally underestimated the neutron streaming. Higher order approximations required extensive computing time approaching that of the Monte Carlo analysis.