This paper shows the analysis of elliptical pressure vessels with circular cross section subjected to internal pressure. Pressure vessels have a very wide range of applications in the propulsion industry and work under very high internal pressures and hence these vessels must be mechanically stable to store the propellant under the required pressure conditions. Therefore, proper analysis of these vessels must be conducted before they can be sent for machining processes. This paper shows analytical solutions as well as Finite Element Solutions to analyse the pressure vessels. A 3D model of a pressure vessel is also created and simulated under required constraints and pressure loads and solved using computational finite element solver. In the end, the results are compared and an attempt is made to restrict the relative error under 5%.