Pressure Vessels are closed containers utilized for storing fluids at certain temperatures and pressures different than ambient conditions. They are used as reactor, convertor, regenerator or splitters. Pressure Vessels are in the form of cylinders, spheres or cones, out of which cylinders are most preferably used. Constructional features of pressure vessels include main body or shell, head, saddles and nozzles. Cylindrical Pressure Vessels are available as either Mono Wall or Multi Layer. Multi Wall, a type of Multi Layer Pressure Vessels is used is manufactured by a process of shrink fitting. When fluids are held at such critical conditions, the shell thickness required by the vessel is higher having high thickness associated with Pressure Vessel imposes its own problems in construction such as bulkiness, high material cost etc. To overcome such drawbacks, Multi Wall Vessels are used. In shrink fitting, thermally expanded shell is fitted over the other shell who is at normal temperature. The system is cooled to achieve the desired interference. This interference creates the necessary compressive stresses within the shells, which are used to counter the tensile stresses developed by the fluids. This reduces Hoop's stresses, making the shell thinner than the shell of Mono Wall Pressure Vessel for same internal pressure. Hence both cost and quantity of material is optimized. The objective of our project is to study Multi Wall Pressure Vessels and code calculations for shell as per the ASME Section VIII, Div.1 and Div.2 for a case study of Pressure Vessel with specific internal pressure. Our wok also includes validation of code calculations using the software ANSYS APDL 15.0.