An evaluation of the computational efficiency of some spatial discretization schemes has been carried out on a number of slab geometry problems of interest in the shielding field. The achievable accuracy for a given cost of the calculation was compared, taking into account that the actual cost depends on both the computing time and the storage required and using as an error measure the ratio to the “reference solution” for a global quantity like the dose rate or the fast flux. The examined cases include neutron calculations in water, concrete, and steel slabs and, in a pressurized water reactor system, the photon calculations in a lead slab. The main conclusion of the study is that, for a given cost, the exponential scheme supplies solutions more accurate than those of the linear characteristic scheme or, at least, of the same quality.