Coated fuel particles, most commonly tri-structural isotropic (TRISO), are intended for application in several designs of advanced nuclear reactors. A complete understanding of the residual stresses and local properties of these particles through their entire lifecycle is required to inform fuel element manufacturing, reactor operation, accident scenarios, and reprocessing. However, there is very little experimental data available in the literature on the magnitude of residual stresses in the individual coating layers of these particles. This work applies ring-core focussed ion beam milling combined with digital image correlation analysis (FIB-DIC) to cross-sections of TRISO and pyrolytic carbon coatings in surrogate coated fuel particles to evaluate the residual stresses. Tensile residual hoop stresses are identified in both pyrolytic carbon layers, while silicon carbide experiences a compressive residual hoop stress. Note that these residual stresses, which were not accounted for in the models reported in open literature, have magnitudes comparable to the stresses predicted to arise in real fuel particles during service. A 2D linear-elastic continuum-based finite element analysis has been conducted to investigate the stress relaxation phenomena caused by sectioning stressed coatings on spherical particles. The FIB-DIC method established here is independent of radiation defects and can be applied to irradiated TRISO particles to retrieve first-hand information regarding the residual stress evolution during service.