The uncertainties of model parameters, structural geometry, material property, and external force of the polymer bonder explosive, were quantified with probability box and propagated with nested sampling method in order to separate the different effect of aleatory uncertainty and epistemic uncertainty on response of interest. Moreover, numerical error and model form error were also quantitatively superposed to acquire the response uncertainty and the reliability interval of the polymer bonder explosive (PBX) structure consequently. In addition, the results of proposed method in this paper were compared with the determinate checking method and the probabilistic reliability method. It is indicated that the reliability assessment with the consideration of uncertainty can reduce the engineering risk than the determinate method. Furthermore, the reliability interval obtained by the proposed method covers the reliability calculated by probabilistic method, and can narrow down to the true reliability as the epistemic uncertainty decreases.