The intention of this report is to use computer simulations to investigate the viability of two materials, water and polyethylene, as shielding against space radiation. First, this thesis discusses some of the challenges facing future and current manned space missions as a result of galactic cosmic radiation, or GCR. The project then uses MULASSIS, a Geant4 based radiation simulation tool, to analyze the effectiveness of water and polyethylene based radiation shields against proton radiation with an initial energy of 1 GeV. This specific spectrum of radiation is selected because it a component of GCR that has been shown by previous literature to pose a significant threat to humans on board spacecraft. The analysis of each material indicated that both would have to be several meters thick to adequately protect crew against the simulated radiation over a several year mission. Additionally, an analysis of the mass of a simple spacecraft model with different shield thicknesses showed that the mass would increase significantly with internal space. Thus, using either material as a shield would be expensive as a result of the cost of lifting a large amount of mass into orbit.