In this research, a composite pressure vessel with a liner under internal pressure is investigated. Stress analysis is performed using a computer code written in MATLAB. Therefore, the stress components in the composite part of the studied vessel are extracted using the classical lamination theory (CLT) and then the occurrence of failure in the most critical layer is examined using the Hashin failure criteria. thus, the failure pressure associated with the first-ply-failure is obtained. Then, based on the ply-discount method in the context of continuum damage mechanics, the mechanical properties of the damaged layer are reduced and the stress analysis is performed again and the vessel failure is evaluated. This process repeats until all the layers experience failure and final pressure is reported as burst pressure. In the next step, by considering manufacturing-induced uncertainties and applying Monte Carlo method, the failure pressure of the vessel is obtained and the influence of uncertainties on the results is also studied. In this study, the parameters of fiber volume fraction and fiber orientations are assumed as the uncertainties. Comparison of the results with the experimental data indicates the accuracy of this method. Then, the reliability of each layer of the composite pressure vessel is studied using the first-order reliability method and finally, the Monte Carlo simulation is used to validate the results.