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A novel two-dimensional model is presented for multiaxial thermal stresses, elastic strains, creep strains, and creep energy density at the interfaces of solder joints in leadless chip resistor (LCR) assemblies. The model is applicable to both plane stress and plane strain conditions, and incorporates both global and local expansivity mismatches. Interfacial thermal stresses are approximated using elementary strength of materials theory under arbitrary time-dependent thermal loading. Partial differential equations are linearized through a simple finite difference discretization procedure. The model is mathematically straightforward, and can be extended to include plastic behavior and problems involving external loads and a variety of geometries. The paper presents comparisons with finite element results and considers the mechanics of solder creep accumulation and stress relaxation as predicted by the model.