Currently spacecraft uses aluminum alloys for primary structures which do not provide sufficient radiation protection for both the spacecraft electronics and for the astronauts in cislunar space. This thesis evaluates the shielding effectiveness of several types of polymer composite materials against Galactic Cosmic Rays (GCRs). Because the galactic cosmic rays consist of high energy particles and produce neutrons while interacting with shielding materials, the purpose of this thesis is to assess new shielding materials that could be used to protect spacecraft electronics and the astronauts against both primary and secondary radiation. New type of composite shielding materials which are metal-doped polyacetylene with hydrogen are studied. Since the metal doped polyacetylene have large molecules, they are proposed to be ideal hydrogen storage materials for shielding purposes. The MULASSIS which is a one-dimensional Monte Carlo transport code is used for the dose equivalent calculations. This transport code demonstrated that the shielding effectiveness of the proposed materials in this thesis are better when compared with the currently used ones. In addition, the fluence analysis shows that Ti-decorated cis-polyacetylene with hydrogen content produces less neutrons when it interacts with GCR radiation and thus it naturally becomes very effective shielding material.