Shielding is the only practical countermeasure for the exposure to cosmic radiation during space travel. It is well known that light, hydrogenated materials, such as water and polyethylene, provide the best shielding against space radiation. Kevlar and Nextel are two materials of great interest for spacecraft shielding because of their known ability to protect human space infrastructures from meteoroids and debris. We measured the response to simulated heavy-ion cosmic radiation of these shielding materials and compared it to polyethylene, Lucite (PMMA), and aluminum. As proxy to galactic nuclei we used 1 GeV n iron or titanium ions. Both physics and biology tests were performed. The results show that Kevlar, which is rich in carbon atoms (about 50% in number), is an excellent space radiation shielding material. Physics tests show that its effectiveness is close (80-90%) to that of polyethylene, and biology data suggest that it can reduce the chromosomal damage more efficiently than PMMA. Nextel is less efficient as a radiation shield, and the expected reduction on dose is roughly half that provided by the same mass of polyethylene. Both Kevlar and Nextel are more effective than aluminum in the attenuation of heavy-ion dose.