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This paper provides elastic analysis of compressive stresses in the matrix and skin regions of automotive substrates during 3D- and 2D-isostatic strength testing. The matrix region is treated as transversely isotropic material and the skin region as isotropic material, each with their independent elastic properties. Such a solution helps quantify load sharing by the matrix and skin regions which, in turn, affect compressive stresses in each region. The analysis shows that the tangential compressive stresses in the skin and matrix differ significantly at the interface due to high stiffness ratio of skin versus matrix. The resulting strain in the skin is more severe for thin and ultrathin wall substrates and may lead to localized bending of interfacial cells thereby inducing premature failure. Methods to reduce compressive strain in both the matrix and skin without affecting performance-related advantages are discussed.