A pressure vessel is a closed container designed to hold gases or liquids at a pressure substantially different from the ambient pressure. The main objective the thesis work is to make an analysis and optimize the location and size of opening hole in a pressure vessel cylinder. For the purpose of analysis and optimization, three thick-walled cylinders with different internal diameters and having same height and thickness are chosen. Further hole diameter is varied and positioned at the center of each cylinder for hole size optimization, also hole of particular size is placed at different pressure vessels surface locations. It is found that with the increase in diameter of hole, Von Misses initially decreases and then becomes constant with hole size. Finally optimum locations of the hole was found.