Composites are materials created by dissimilar materials with a view to improve the properties or to create materials with desired properties. Advanced Fiber Reinforced Polymer Composites have emerged as an important class of engineering materials for load bearing applications with all round properties for many engineering and social applications. Filament Wound structures such as pressure bottles, pipes and motor cases are widely used in aerospace applications. Traditionally, pressure vessels were constructed from isotropic materials such as steel and aluminum. Structures made of isotropic materials are less efficient since the longitudinal stresses use only half that of the structure capabilities but now, with the advent of composites, the material can be tailored so that more fibers are laid in the direction where the stresses are high. The versatility of filament winding saves weight by tailoring the winding patterns to carry the loads. This is particularly advantageous in closed end pressure vessels where the longitudinal loads are only half that of the hoop loads. Composite pressure vessels developed by filament winding technology fall into two categories i.e., Pressure vessels with equal pole openings and unequal pole openings. Usually Composite Pressure Vessels with equal pole openings can be developed with Geodesic paths. Geodesic lines connect two points along the shortest distance over the surface. In this case no friction force is required to keep the fiber from slipping, since it follows a self-stable trajectory. There are, however situations where it is not possible to place fibers, at least in some regions of the mandrel, on the geodesic curve. It implies that we have to resort to modified helical winding (non-geodesic) at cylindrical portion or end domes or both. A composite Pressure Vessel like CRMC (Composite Rocket Motor Case) with unequal pole openings is an example of this. The design procedure of non-geodesic filament wound pressure vessel involves varying friction factors on the shell. In the present study, a composite pressure vessel with a non-geodesic fiber trajectory for the entire shell is considered. The composite pressure vessel comprises of inner rubber lining, metallic polar bosses and composite shell layers with variable thickness and orientation of the fiber. The shell is subjected to uniform internal pressure and the conditions of thin walled structure and balanced symmetry winding pattern are adopted. The deviation fr...