This paper reviews some of the critical considerations that are important during the design of high-pressure vessels. These critical considerations include Stress Concentration Factors (SCF), measurement of stress distribution, and geometric design parameters affecting stress concentration in the design of pressure vessels with a specific focus on thick compound cylinders. Further, the motivation of this study is to analyze stress concentration that occurs after the provision of cross bores in pressure vessels. Stress analysis can be performed using experimental, analytical, and numerical techniques. Hence, the study concluded that there is no known analysis carried out on the effects of cross bores on thick compound cylinders using Finite Element Analysis (FEA). Thus, there is need for understanding the effects of optimization of geometric parameters of cross bore size, shape, location, obliquity and thickness ratio, in the design of thick compound cylinders.