This thesis reports the results of a preliminary design of a nanocomposite overwrapped pressure vessel (NOPV). The NOPV consists of a titanium liner helically overwrapped with a Polyacrylonitrile (PAN) Single-Walled Carbon Nanotube (SWCNT) fiber in an epoxy matrix. Micromechanics models were used to predict the mechanical properties of the PAN-SWCNT/EPOXY composites. A MATLAB code based on an elasticity solution was developed to analyze the stresses and deformations of multilayered filament wound pressure vessels under internal pressure. A case study on the helium pressurization tank used in the National Aeronautics and Space Administration's (NASA) Jet Propulsion Laboratory (JPL) Messenger Spacecraft was performed to assess the nanocomposite performance. Comparisons between the Toray 1000 advanced filament composites currently in use and the proposed nanocomposites were made. The study shows that the NOPV offers advantages in mass reduction. Such reduction is a common goal in aerospace design. In addition, parametric studies were also conducted to determine the optimal configuration of the proposed NOPV.