Safety is the prime consideration in the design and manufacture of high pressure containers. Therefore, quality analysis of container strength in withstanding internal pressurization is a vital issue. This work has investigated cylindrical high pressure containers. The FE method was applied to analyze the effect of thickness, height, outer diameter and workpiece material on the container strength in withstanding internal pressurization. Weakening spots and fractures were predicted. The Taguchi method was further applied to evaluate the optimum design of the structure of high pressure containers.