In the past, steel structures were vastly used in various applications to carry high loads. To avoid difficulties caused by steel, such as high weight, other materials like Aluminum, Titanium and composites have been proposed. The use of laminated composite shells in many engineering applications has been rapidly expanded in the past four decades due to their higher strength and stiffness to weight ratios as compared to most metallic materials. Composite shells are used increasingly in areas such as automotive engineering, biomedical engineering and other applications. In this study, stress, fracture, and buckling analysis of composite pressure hull are discussed. In chapter one, after studying history of stress and fracture analysis of composite shells, background of buckling analysis of cylindrical and spherical shells and also winding pattern methods have been reviewed. In chapter two, composite materials are introduced and categorized. Advantages of composite materials in comparison with other materials and their stress-strain curves are described. Applications of composites in automobile, bio-engineering, public toys, artificial limbs and other industries are mentioned. Moreover, manufacturing procedures of composites are briefly introduced. Finally, stress-strain relations of composites are explained. In chapter three, entitled "filament winding of composites", composite manufacturing processes are studied and various types of filament winding are discussed in details. Furthermore, equations of Geodesic, Isotensoid, and planar winding patterns are investigated. In chapter four, various theories of composite failure are explained and Puck's failure theory has been chosen as the best criteria for detecting failure onset. Then, equations of this criteria are derived. In chapter five, filament wound pressure hull with Geodesic and planar patterns have been simulated by the finite element method. In the simulations, python scripting is used to achieve more accurate modeling of angle and thickness variations. In this chapter, the effects of winding angle and aspect ratio parameters on pressure hull strength are explored. Geodesic winding pattern with aspect ratio of 1.2 and winding angle of 45 degree have been selected as the best winding conditions for pressure hull. Finally, based on Puck's criteria, a user made subroutine for detecting onset of failure has been prepared. This program is verified by available results and used for failure analysis of optimum composite pressure hull. The results show that a composite pressure hull can carry considerable external pressure even after failure initiation due to stress redistribution in the laminates. Keywords: Composite pressure hull, Planar winding, Geodesic winding, Puck's failure criteria