In its most general form, a pressure vessel consists of two main parts; the cylindrical part and the dome part. This paper presents the analysis that has been conducted in order to obtain the optimum shape of the filament wound dome part. A composite pressure vessel with optimized dome ends avoids critical stresses that are incorporate with the structure when the structure is internally pressurized. The analysis deals with domes with/without polar opening. Analytical models are developed based on mechanics of materials, geodesic analysis and are solved using numerical techniques. The models can predict both the optimum shape and optimum thickness of the dome part that can safely withstand the applied loads with minimum weight. The results have been verified using published work with good agreement. Finally, the models have used to investigate the effect of changing material type, material properties on the optimum shape of the dome part.