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According to the mathematical formalism of the eigenfunction expansion method, the problem of stress-singularities arising from multi-material junctions is addressed. The wedges are composed of isotropic homogeneous materials and are in a condition of plane stress or strain. The order of the stress-singularity is provided for tri-material junctions, paying special attention to the role played by Mode-I and Mode-II deformation. The effect of cracks inside either the softer or the stiffer material is also investigated. Numerical results can be profitably used for establishing optimum material configurations.