The longevity of solid oxide fuel cells is influenced by internal residual stresses, which may induce deformation or fracturing of components. This study investigates the residual stress distribution at the nonplanar cathode–electrolyte interface by approximating the actual interface with trigonometric functions and developing a three-dimensional (3D) model. The model reveals that the stress patterns at nonplanar interfaces can elucidate the genesis of interfacial cracks. During fabrication, anode contraction results in compressive stress within the electrolyte and tensile stress within the anode, with thermal discrepancies between layers being the primary cause of residual stresses. The reduction process diminishes these stresses, thus enhancing the mechanical integrity of the cell. Mitigating interface nonplanarity is beneficial for minimizing residual stress. At each interface crest, the electrolyte exhibits a local minimum in compressive stress, and a local maximum in shear stress occurs between each crest and trough. Furthermore, decreasing the initial porosity and NiO volume fraction can slightly lessen interlayer thermal discrepancies, with little effect on residual stresses.