This paper provides detailed insights into the external pressure vessels. External pressure vessels are designed to perform under extreme operating conditions, so the selection of material and geometry along with stress analysis are fundamental for their optimal efficiency. The objective of this research is to provide a case study of the material, design, and stress generated in the pressure vessel to make it suitable for thermal and load-bearing applications in the aerospace industry. An aluminum alloy was chosen as the design material due to its low density and high strength. The modeling geometry of the alloy was constructed using the ASME section-VIII division-I div code. After the performed Finite Element Analysis (FEA), modeling was carried out deploying the ANSYS design modeler to obtain the stress concentration and failure mode of the model. The present study demonstrates the behavior of a structure under applied load and identifies the weak areas of its geometry. Based on the external stress at the center of the structure, the maximum and minimum stresses computed are 0.763 MPa and 0.00803 MPa, respectively. It was also found that the maximum strain is generated at the center of the structure and is equal to 1.0834e-6 mm/mm, the maximum deformation is equal to 0.00109 mm and also occurred at the center, while the shells of the model are unable to undergo any deformation. FEA results agree with the analytical results, as the errors for hoop stress and equivalent strain are 4.8% and 1.8%, respectively. Thus, the proposed method can be applied to predict the equivalent stress, equivalent strain, total deformation, and stress intensity, which are required for the structural integrity analysis of pressure vessels.