The solution of the periodic problem for layered composite structure on the discretely located linear-elastic bearings has been obtained in the paper (Starushenko, 2000). The general case of the problem is considered in this paper. The structure that is located on the combined continuous and discrete elastic foundation is examined. The foundation rigidity is periodically changed in the composite phase limits. The structure is fortified by elastic supports in the component part junction. The problem is solved for general problem statement. It is supposed that physical and geometrical characteristics of the body and elastic foundation can accept any value. The periodic solution of the problem has been obtained in components of displacement function by means of saw-tooth argument transformation method in the paper. Analysis of obtained solution has been carried out. The flexure functions of the elastic foundation depending of the structure rigidity and geometric factors have been found.
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