Anisotropic composite cylinders and pressure vessels have been widely employed in automotive, aerospace, chemical and other engineering areas due to high strength/stiffness-to-weight ratio, exceptional corrosion resistance, and superb thermal performance. Pipes, fuel tanks, chemical containers, rocket motor cases and aircraft and ship elements are a few examples of structural application of fiber reinforced composites (FRCs) for pressure vessels/pipes. Since the performance of composite materials replies on the tensile and compressive strengths of the fiber directions, the optimum design of composite laminates with varying fiber orientations is desired to minimize the damage of the structure. In this study, a complete mathematical 3D elasticity solution was developed, which can accurately compute stresses of a thick multilayered anisotropic fiber reinforced pressure vessel under force and pressure loadings. A rotational variable is introduced in the formalism to treat torsional loading in addition to force and pressure loadings. Then, the three-dimensional Tsai-Wu criterion is used based on the analytical solution to predict the failure. Finally, a global optimization algorithm is used to find the optimum fiber orientation and their best combination through the thickness direction.