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Mathematical modelling for stress-strain state of Layer-by-Layer (LbL) solids is the subject of present communication. LbL solids are produced by synthesizing of multilayered thin film structures on deformable substrate. Open-ended questions, both in theory and in technology, are associated with ultra-thin and thick (multilayered) coatings. Problems with thick and multilayered coatings are mainly characterized by incompatible deformations and significant residual (internal) stresses, which lead to the destruction of the whole structure.