Mathematical models of heat flow and elastic stress generation based on the finite-element method have been developed and utilized to analyze the Epic-3 Monofrax-S casting process (Monofrax-S is primarily composed of 47-57% A1₂O₃, 34-41% ZrO₂ and 10-15% SiO₂). The results of the mathematical analysis, in conjunction with information obtained from a comprehensive industrial study, has led to the development of mechanisms for the formation of the various crack types found in this casting process. Thermal stresses have been predicted to be generated early in the solidification process in association with rapid cooling of the refractory surface as it contacts the initially cool mould and again later in the solidification process in conjunction with the tetragonal-to-monoclinic phase transformation which occurs in the zirconia component of Monofrax-S. The mathematical analysis has also helped to identify indirectly a potential mechanism for the generation of mechanical stresses. Based on an understanding of the generation of tensile stresses, recommendations have been made for modifications to the moulding and casting procedures in order to reduce the propensity for the formation of cracks. The modifications have included changes to the mould construction and geometry to reduce the generation of mechanical stresses and changes to the moulding materials to impact on the flow of heat at key times during solidification and cooling. With the recommendations in place, the casting rocess has been re-examined with the mathematical models to verify the impact of the modifications. The predictions show that the modifications have acted to reduce tensile stresses associated with the formation of Type-A and -B cracks. Preliminary industrial trials with the modified mould have yielded blocks free of these defects.