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Composite structures, especially pressure vessels, pipelines, and additional components such as tees, reductions, or inspection openings are more and more willingly used in the chemical industry. In this research, a novel design of a low-pressure composite vessel with an inspection opening is presented. The vessels are unsymmetrical considering the domes. On one side the opening is considerably bigger, around half of the cylindrical diameter of the vessel. This design requires a new approach to manufacturing such structures. In this study, a two-step analysis was performed. Firstly, small-size pressure vessels (S) were manufactured and the design of dome reinforcement was validated. Then, the final design of vessel (M) was produced, with a volume of around 700 litres. The vessels were initially calculated for 21 bars of burst pressure. During burst pressure tests, the strains were measured with optical fibres (FBG) and strain gauges. Additionally, the acoustic emission was utilized to predict the damage modes and locations. Finally, a microscopic evaluation of the specific parts of the vessels was performed. Conclusions were drawn, that the proposed novel design of dome reinforcement around the inspection opening fulfilled the strength and stiffness requirements.