This paper formulates and solves the problem of model identification and parameter uncertainty in plutonium storage systems. A systematic procedure helps to choose among alternative mathematical models with different properties and degrees of freedom. Rigorous metrics for measuring the statistical alignment between five different physical models and given experimental data are discussed. On the basis of those metrics, the most adequate model is identified and the optimal parameter values for the heat source and the heat transfer coefficients in the packed plutonium bed are calculated. Model confidence and parameter uncertainty are accurately quantified by confidence regions. Rigorous bounds on the uncertain parameter range are computed. Mathematical framework for a flexible design approach and risk minimization is introduced. Flexibility analysis approach is used to detect the worst case temperature hotspots in plutonium storage containers.