Single-crystal nickel-base superalloys are often used in the hot sections of gas turbines due to their good mechanical properties at high temperatures such as enhanced creep resistance. However, the anisotropic material properties of these materials bring many difficulties in terms of modelling and crack growth prediction. Cracks tend to switch cracking mode from Mode I cracking to crystallographic cracking. Crystallographic crack growth is often associated with a decrease in crack propagation life compared to Mode I cracking and this must be taken into account for reliable component lifing. In this paper a method to evaluate the crystallographic crack propagation rate related to a crystallographic crack driving force parameter is presented. The crystallographic crack growth rate is determined by an evaluation of heat tints on the fracture surface of a specimen subjected to fatigue loading. The complicated crack geometry including two crystallographic crack fronts is modelled in a three dimensional finite element context. The crack driving force parameter is determined by calculating anisotropic stress intensity factors along the two crystallographic crack fronts by finite-element simulations and post-processing the data in a fracture mechanics tool that resolves the stress intensity factors on the crystallographic slip planes in the slip directions. The evaluated crack propagation rate shows a good correlation for both considered crystallographic cracks fronts.