Multilayer systems are generally subjected to thermal stresses because of the thermal mismatch between layers, and localized stresses normal to interfaces; i.e., interfacial peeling stresses, exist at edges because of the free-edge effect. These peeling stresses can result in mode I edge delamination. However, because of the complexity of the problem, exact closed-form solutions for peeling stresses are unattainable, even for bilayer systems. As a result, the peeling moment resulting from these localized peeling stresses was proposed recently as an alternative to study edge delamination. Exact closed-form solutions for the peeling moment at each interface in multilayer systems are derived in the present study, and approximate solutions for the special case of multilayer of thin films on a thick substrate are also presented. Specific results are calculated for GaAs/Si bilayers and GaP/GaAs0.5P0.5/GaAs trilayers. However, the present solutions are readily to be applied to any elastic multilayer system for characterizing mode I edge delamination by thermal stresses.