In this paper, carbon fiber and Kevlar R fiber woven composites were investigated as potential cryogenic tank materials for storing liquid fuel in spacecraft or rocket. Towards that end, both carbon and Kevlar R fiber composites were manufactured and tested with and without cryogenic exposure. The focus was on the investigation of the influence of initial cryogenic exposure on the degradation of the composite. Tensile, flexural and inter laminar shear strength (ILSS) tests were conducted, which indicate that Kevlar R and carbon textile composites are potential candidates for use under cryogenic exposure.