Filament winding technology is widely used to manufacture high-strength composite pressure vessels, especially in aerospace, where metal inserts are often integrated into the polar regions to reinforce structural integrity. However, these inserts introduce localized stress concentrations that can impact load-bearing capacity and vessel reliability. This study aims to analyze stress distribution patterns and identify the main factors contributing to the failure of composite pressure vessels with metal inserts. Using finite element analysis (ANSYS), three models were created to simulate the stress-strain state in the polar regions under various contact conditions and internal pressures. The models, which represented multilayered carbon composite and rubber shells, assessed contact interactions between inserts and composite layers. Specifically, rear polar opening models represented two extreme insert connection cases: rigid connection and complete lack of adhesion. The maximum stress concentrations were identified in the outer layers of both the front and rear domes, particularly in regions with minimal bonding between metal and composite layers. In cases without bonding, stresses along the winding in the rear dome layers were found to be 1.62 times higher than with bonding. Simulation results showed that adjustments to insert parameters—such as thickness, taper angle, and flange projection—effectively reduced stress levels and contact pressures. Optimized insert designs achieved up to a 50% reduction in stress concentrations, improving load distribution. The study highlights the critical importance of metal insert geometry in sustaining structural integrity. By optimizing insert design, stress concentrations are reduced, failure risks are minimized, and vessel durability is enhanced.