Integral shielding experiments using iron-polyethylene slab shields were carried out to determine an optimum arrangement for the neutron dose rate. The total thickness of the iron slabs was fixed at 32 cm, while several thicknesses of polyethylene slabs were employed as a parameter. Some measured data were analyzed by the Monte Carlo code MORSE-CG with the splitting technique. Depending on the location of the polyethylene slab, the measured neutron dose rates changed remarkably in the iron-polyethylene shielding system. When the polyethylene slab was 1 cm thick, the ratio of the maximum neutron dose rate to the minimum value was 1.3, and the ratio was increased to as much as 5.4 for the 14-cm-thick polyethylene slab. The minimum dose point (i.e., optimum shielding arrangement) was observed when the polyethylene slab was located near the detector with the iron slab placed near the neutron source. This was also demonstrated by the Monte Carlo calculations.