Residual stress plays an important role in the formation and growth of cracks in thermal barrier coatings and single-crystal superalloy substrates. In this study, a finite element model for a planar double-layer thermal barrier coating and a crystal plasticity finite element model based on dislocation slip-induced plastic deformation of single-crystal materials were established to analyze the residual stress in the coatings and the substrate, considering the creep and crystal plasticity of the substrate materials. The simulation results show that the thermal barrier coatings bear most of the stress generated by high temperatures, and the residual stress of the substrate is small. By comparing the two material properties to calculate the interface stress when the amplitude of the interface between the substrate and the coating is 30 μm and the thickness of the thermal grown oxide layer is 5 µm, the interfacial stress of the substrate at the macro scale was found to be similar to the interfacial stress at the micro slip system scale. Based on the cumulative shear strain, it was determined that the [001]-, [011]-, and [111]-oriented alloys activated the 12, 8, and 4 groups, respectively, under the combined action of thermal stress and centrifugal force of the coating. Comparing the activation of different initial orientation slip systems and the magnitude of the yield stress provides a theoretical foundation to study the structural integrity of single-crystal alloys.