Currently, methods for estimating the pressure-induced vulnerability of nuclear power plant containments and conducting probabilistic safety assessment (PSA) often overlook the uncertainty quantification arising from the propagation of inherent uncertainties. Additionally, traditional engineering demand parameters predominantly focus on local response indices, failing to adequately consider the overall damage evolution of the nuclear containment structure. To overcome these limitations, an interpretable machine learning (ML) approach was proposed to adequately capture the nonlinear features of the overall damage data even with limited sample size. The research findings demonstrate that the framework based on interpretable ML not only enhances the accuracy of the analysis but also effectively quantifies the prediction uncertainties, surpassing traditional linear uncertainty quantification methods. The ML-based method better reflects the relationship between internal pressure and structural damage, while providing more reliable confidence intervals for the pressure-induced vulnerability of nuclear containments and PSA results.