We study uncertainty in blast wave problem. Input uncertainties are characterized as aleatory and epistemic uncertainties. Mixed UQ approaches are employed. The outer level UQ is linked to epistemic uncertainty, and the inner UQ is linked to aleatory uncertainty. Non-intrusive polynomial chaos (NIPC) is utilized to cope with aleatory uncertainty. Dempster-Shafer structure is used to deal with epistemic uncertainties. Upwind scheme is used to solve corresponding deterministic system. It acquires preferably effect. It is shown that NIPC approach and Dempster-Shafer structure handles efficiently effect of initial-boundary value uncertainty and parameter uncertainty on simulation result. It is helpful in evaluating degree of confidence and validating result of modeling and simulation.