This document introduces the compressed hydrogen gas storage technology and gives a computational method to calculate the minimum required material under high pressure conditions of a hydrogen vessel suited for a fuel cell mounted on a bike. Although this thesis focuses in the design of a less than 2 L pressure vessel, this formula can be applied in any storage tank size. Chapter 1 explains why hydrogen is a reasonable energy storage solution on-board and which are the market options for now or in the near future. Chapter 2 studies widely the hydrogen compressed gas and its storage and fueling challenges. Chapter 3 analyze the strict safety tests that are applied to hydrogen pressure vessels on-board. Chapter 4 offers a method to find the optimum stacking and laminate thickness for a pressure vessel under internal pressure. Chapter 5 explains a structural analysis using NX Nastran Laminate Composites simulations. Finally, chapter 6 explains hydrogen transport through polymers and chooses a suited polymer for the function of hydrogen barrier or liner.