The design of future spacecraft such as the Crew Exploration Vehicle must take into account the radiation shielding properties of both the structural components as well as dedicated shielding materials. Since modest depths of shielding stop the vast majority of Solar Energetic Particles (SEP), the greater challenge is posed by the need to shield crew from the Galactic Cosmic Rays (GCR), which include highly-charged and highly-energetic particles. Here, we report on results from tests performed with beams of 1 GeV/nuc 56Fe at the Brookhaven National Laboratory. A wide variety of targets, both elemental and composite, were placed in the particle beams, and the spectra of particles emerging from the targets were measured using a stack of silicon detectors. Results are presented primarily in terms of dose reduction per g cm-2 of target material, and support the conclusions of an earlier calculation by Wilson et al. showing that performance improves as the shield's mass number decreases, with hydrogen being by far the most effective. The data also show that, as depth increases, the incremental benefit of adding shielding decreases, particularly for aluminum and other elements with higher atomic mass numbers.