During hypothetical severe nuclear reactor accidents, structural materials in the reactor vessel can relocate downward and form debris regions above the lower head. A one-dimensional model is presented that considers melt progression in the debris as well as the thermal and mechanical response of the head. Only creep rupture of the lower head is considered; however, other modes of vessel failure can be considered with the methodology developed, and the model can easily be extended to higher dimensions. Numerical solutions are compared with an analytical model developed by T G. Theofanous. The goal of the work is to identify the parameters that most affect the state of the debris at the time of lower head creep rupture. Results of sensitivity analyses presented indicate that melt relocation phenomena, the initial composition profile of the debris, and the pressure inside the vessel are all important. On the other hand, changing the porosity or the particle diameter produces less significant effects because several competing phenomena cancel each other.