The geometric representation and the multidimensional calculational method for neutronics analysis of tokamak reactors with major penetrations have been examined. It has been found that two-dimensional models are useful for scoping studies but that three-dimensional models are necessary for detailed design studies. The material and geometry requirements of local exterior penetration shields are examined. The level of radiation streaming is parametrized as a function of the penetration size and shape. A dual-purpose duct system in which the evacuation (vacuum pumping) ducts are connected to the neutral beam ducts at locations outside the bulk shield is an attractive approach. This system reduces the overall shield requirements and potentially permits orders of magnitude reduction in the radiation level at the vacuum pumps. A comparison of the two plasma supplementary heating methods—radio frequency (rf) and neutral beams—shows that the rf system offers considerable advantage over the neutral beam system in terms of lower shielding requirements and easier control of the radiation dose in the reactor building.