One major obstacle to human space exploration is the possible limitations imposed by the adverse effects of long-term exposure to the space environment. Even before human space flight began, the potentially brief exposure of astronauts to the very intense random solar energetic particle events was of great concern. A new challenge appears in deep-space exploration from exposure to the low-intensity heavy-ion flux of the galactic cosmic rays since the missions are of long duration, and accumulated exposures can be high. Because cancer induction rates increase behind low to moderate thicknesses of aluminum shielding, according to available biological data on mammalian exposures to galactic cosmic ray-like ions, aluminum shield requirements for a Mars mission may be prohibitively expensive in terms of mission launch costs. Alternative materials for vehicle construction are under investigation to provide lightweight habitat structures with enhanced shielding properties. In the present paper, updated estimates for astronaut exposures on a Mars mission are presented and shielding properties of alternative materials are compared with aluminum.