Radiation assessment and protection in space is the first step in planning future missions to the Moon and Mars, where mission and number of space travelers will increase and the protection of the geomagnetic shielding against the cosmic radiation will be absent. In this framework, the shielding effectiveness of two flexible materials, Kevlar and Nextel, were tested, which are largely used in the construction of spacecrafts. Accelerator-based tests clearly demonstrated that Kevlar is an excellent shield for heavy ions, close to polyethylene, whereas Nextel shows poor shielding characteristics. Measurements on flight performed onboard of the International Space Station and of the Foton-M3 capsule have been carried out with special attention to the neutron component; shielded and unshielded detectors (thermoluminescence dosemeters, bubble detectors) were exposed to a real radiation environment to test the shielding properties of the materials under study. The results indicate no significant effects of shielding, suggesting that thin shields in low-Earth Orbit have little effect on absorbed dose.