The “Phase-Field Model of Dislocations” (PFMD) was used to simulate shearing of gamma-prime precipitate arrays in single crystal turbine blade superalloys. The focus of the work has been on the cutting of the L12 ordered precipitates by a<112>{111} dislocation ribbons during Primary Creep. The Phase Field Model presented incorporates specially developed Generalised Stacking Fault Energy (γ–surface) data obtained from atomistic simulations. The topography of this surface determines the shearing mechanisms observed in the model. The merit of the new γ–surface, is that it accounts for the formation of extrinsic stacking faults, making the model more relevant to creep deformation of superalloys at elevated temperatures.