Neutron penetration in water and in iron/water shields has been calculated using a P-3 multigroup program. The thermal-neutron flux from a point fission source in water obtained from calculation and experiment agree to within 18% in the region between 15 and 140 cm, covering more than 9 decades of attenuation. The calculated neutron spectrum compares favorably in shape and magnitude with moments-method results out to 120 cm of water. The observed variations of the thermal-neutron flux in an iron/water shield are predicted by the P-3 program. Some of the differences between experiment and the predicted thermal flux within a thick iron region are due to the single-energy-group treatment in the calculations. Uncertainties in the high-energy cross sections for iron are of sufficient magnitude to account for differences between calculation and experiment noted in the water region following iron.