Stresses normal to interfaces, i.e., interfacial peeling stresses and interfacial shear stresses, exist locally at edges of multilayers because of both the thermal mismatch between layers and the free-edge effect. These peeling and shear stresses can result in modes I and II edge delamination, respectively. However, because of the complexity of the problem, exact closed-form solutions for these stresses are very difficult if not impossible to derive even for bilayered systems. Hence, instead of the detailed stress field at edges, both the interfacial peeling moment resulting from the localized peeling stresses and the interfacial shear force resulting from the localized shear stresses are analyzed here. Exact closed-form solutions for the peeling moment and the shear force at each interface in elastic multilayered systems are derived. To illustrate the application of present closed-form solutions, specific results are calculated for five-layered thermal barrier coating systems, and a finite-element analysis is also performed to confirm the analytical results.