The various options and trade-offs in the nuclear design of the blanket/shield for a Tokamak Experimental Power Reactor (TEPR) are investigated. The TEPR size and cost are particularly sensitive to the blanket/shield thickness, ΔBS, on the inner side of the torus. Radiation damage to the components of the superconducting magnet and refrigeration power requirements set lower limits on ΔBS. These limits are developed in terms of TEPR desigpi parameters such as the wall loading, duty cycle, and frequency of magnet anneals. The study of the nuclear performance of various material compositions shows that mixtures of tungsten, or tantalum, or stainless-steel alloys and boron carbide require the smallest ΔBS for a given attenuation. This ΔBS has to be doubled if the low induced activation materials graphite and aluminum are used. The space problems are greatly eased in the Argonne National Laboratory ANL-TEPR reference design by using two separate segments of the blanket/shield. The inner segment occupies the region of the high magnetic field, uses very efficient attenuators (tungsten- or tantalum- or stainless-steel-boron carbide mixtures), and is only 1 m thick. The outer blanket/shield is 131 cm and consists of an optimized composition of stainless steel and boron carbide. For the design parameters of 0.2 MW/m2 neutron wall loading and 50% duty cycle, the reactor components can operate satisfactorily up to (a) 10 yr for the stainless-steel first wall, (b) 10 yr for the superconductor composite after which magnet warmup becomes necessary, and (c) 30 yr for the Mylar insulation. Nuclear heat generation rates in the blanket/shield and magnet are well within the practical limits for heat removal.