Present simple means of accounting for neutron attenuation by metal shields that are followed by relatively thin hydrogenous shields often result in costly overdesign. Alternatively, the shield designer must perform detailed neutron transport calculations. This paper presents a method that uses high-order SN transport in simple geometry to derive an effective removal cross section suitable for point-kernel design calculations. The method involves calculating the fast-neutron biological dose at various spatial points in a hydrogenous shell surrounding metal spheres of various radii, and then finding exponential functions to represent the attenuation of the metal for parametric thicknesses of the hydrogenous material. Specific calculations were performed for lead and polyethylene, with a Po:Be source, using one-dimensional S8 calculations with an asymmetric angular quadrature biased toward the forward direction. Multitable thirty-group cross sections with P3 anisotropic scattering were used for all materials. Results for finite and essentially infinite polyethylene thicknesses were compared; the effect of backscatter on the effective removal cross section is negligible (<1%). The resulting removal cross section was fit by a simple analytical expression within 1.4% for polyethylene thicknesses between 3 and 41 cm. Removal cross sections were derived for lead thicknesses between 0 and 60 cm, but probably are applicable beyond 60 cm. The asymptotic value of the calculated removal cross section is well within the experimental error of the published value for a fission spectrum. The method is not restricted to any particular source spectrum, hydrogenous material, or attenuating material, as has been shown in test calculations for a Ra:Be source and for water, as well as by subsequent successful employment of the method by others for a fission spectrum and in iron shields.