The safe containment of molten core debris following a hypothetical meltdown accident in a light water reactor depends on the post-accident distribution and freezing of the debris on cold core structures. A one-dimensional physical model was developed to study the transient freezing of the molten debris on the inner surface of the test shroud wall in a severe, reactivity initiated accident in-pile experiment, and to assess the potential for wall melting upon being contacted by the molten debris. The conditions of finite wall thickness, convective cooling at the wall outer surface, radiative cooling of the debris, temperature-dependent thermophysical properties, and internal heat generation in the debris were considered. It is concluded that the shroud wall should not melt upon contact by the molten debris, which agreed with the experimental observations, because of the initial low temperature of the wall (538 K) and of the molten debris (∼3500 K) at the time of contact. Should wall melting occur, however, the wall molten layer would be unstable because of the small thickness of the wall and the continuous cooling at the wall outer surface by coolant bypass flow. The agreement between the calculations and experimental results indicated that considering the molten debris during the freezing process as a homogeneous mixture of the constituents (UO2 and Zircaloy) was a reasonable assumption.