Production of gas turbines for jet propulsion and power generation requires the manufacture of turbine blades from single crystal nickel-based superalloys, most typically using investment casting. During the necessary subsequent solution heat treatment, the formation of recrystallised grains can occur. The introduction of grain boundaries into a single crystal component is potentially detrimental to performance, and therefore manufacturing processes and/or component geometries should be designed to prevent their occurrence. If the boundaries have very low strength, they can degrade creep and fatigue properties. The root cause for recrystallisation is microscale plasticity caused by differential thermal contraction of metal, mould and core; when the plastic deformation is sufficiently large, recrystallisation takes place. In this thesis, numerical and thermo-mechanical modelling is carried out, with the aim of establishing computational methods by which recrystallisation during the heat treatment of single crystal nickel-based superalloys can be predicted and prevented prior to their occurrence. This work shows that recrystallisation is most likely to occur following 1.5-2.5% plastic strain is applied at temperatures between 1000oC and 1300oC. This emphasises that high temperature deformation is more damaging than low temperature deformation.