The Three Mile Island Unit 2 accident resulted in the melting of ∼47% of the reactor core and the relocation of ∼15% of the core onto the lower head of the reactor vessel. The severity of the accident has raised questions about the margin of safety against rupture of the reactor vessel lower head in this accident since all evidence seems to indicate no major breach of the vessel occurred. Scoping heat transfer analyses of the relocated core debris and lower head have been made based on assumed core melting scenarios and core material debris formations while in contact with the lower head. The structural finite element creep rupture analysis of the lower head using a temperature transient that was judged to be a challenge to the structural capacity of the reactor vessel is described. This evaluation of vessel response to the imposed temperature transient has provided insight into the creep mechanisms of the vessel wall, a realistic mode of failure, and a means by which margin to failure can be evaluated once examination provides estimated maximum wall temperatures. Suggestions for more extensive research in this area are also provided.