Physically-based models are often used to model changes in geometry and the associated stress fields of graphite moderator bricks within an advanced gas-cooled reactor (AGR). These models require inputs that describe the loading conditions, and coded relationships describing the behaviour of material properties. Material relationships are primarily based upon data obtained from inspection campaigns at operating reactors. However, the data from trepanning campaigns do not provide information on some of the key relationships and parameters that affect the internal stresses generated within the moderator bricks. In this work we explore how uncertain material property relationships affect the internal brick stresses in early- and late-life. We describe two computer experiments designed to study early- and late-life brick stresses and report the results from global sensitivity analysis of the models. The work makes use of an emulator, a surrogate for the FE model, in order to make the sensitivity analyses computationally feasible.