A survey of neutron-attenuating materials is conducted, followed by a systematic optimization of the radiation shield configuration for the Affordable Fission Surface Power System. Water, borated water, boron carbide, boron-doped beryllium, zirconium hydride, and lithium hydride are evaluated for neutron shielding, and tungsten is considered for gamma shielding. Lithium hydride, borated water, and boron carbide are selected for further consideration, and radial, upper axial, and lower axial shield sections are developed separately from these materials and then combined to form complete shields. Two competing effects determine the optimal position of the tungsten layer: increasing secondary gamma production due to fast neutron scattering when the tungsten layer is placed closer to the core, and radially increasing mass when placed farther from the core. The optimal position of the tungsten layer is found for each shield configuration and material. The as-landed configuration of each radiation shield allows a maximum dose of 5 rem/yr to an outpost 1 km from the reactor core. The shield also protects the SmCo magnets in the alternators of the Stirling power converters, allowing a maximum dose of 2 Mrad gamma and 1014 n/cm2 fast neutron fluence to the magnets over the 8-yr design lifetime. A minimum mass is found for each shield section while meeting these dose limits. The radial shield section is cylindrical, and the upper and lower axial shield sections are conical in shape. Axial shields with a range of pitch and thickness are analyzed, and the optimal shapes of the upper and lower axial shields for each material are found. The three sections of the shield are combined to form a complete shield. The lithium hydride shield is the lightest of the final shields at 6215 kg. The borated water shield is the second lightest at 6663 kg, which is 448 kg more than the lithium hydride shield. The boron carbide shield is the most massive at 8315 kg, which is 2100 kg more than the lithium hydride shield.