A pressure vessel is defined as a closed container designed to hold gases or liquids at low pressure than the ambient pressure. The pressure vessel containing fluid (liquid/gas) resists the pressure distribution produced by the fluid equally in all direction on its wall and end of the pressure vessels. Because of the internal loading due to fluid pressure, stresses are generated at different sections of the walls. The various use of pressure vessels are in boiler making industries, chemical industries, petroleum industries and also used in engine cylinders. Two connected pressure vessel design has simulated during its operating condition using COMSOL Multiphysics simulation software. Maximum stress and displacement has derived by solving the mathematical equation under pressure loading condition.