The mathematical models, integral equations and the corresponding numerical schemes, required for thestudyofthestressstateofplatescontainingthincrookeddefectsareconsideredandexplicitlywritten.Theresults obtained using the proposed line model for a circular arc inclusion are in good agreement with those obtained by the direct approach. Numerical examples are also presented for S-like and kinked inclusions. The study of the stress fields of thin objects, one or two dimensions of which are much smaller than the third one (such as boundary layers, flow lines in plasticity, and thin solids introduced into the continuum) is a practi- cally important and mathematically challenging problem, the solution of which usually involves the development of the new mathematical models, methods, and approaches. This statement is proved by the scientific heritage of Il'yushin(1,2),whohadanintensemathematicalinterestinsuchdifficultandveryimportantscientificandtechnical problems. The technology of sheet metal formation has been developed based on Il'yushin's theory of thin-layer flow of metals. Il'yushin's law of plane sections in aerodynamics at supersonic speeds allowed the reduction of the three-dimensional problem of a gas flow around a thin profile to a two-dimensional problem, and then, transferring these results to a plastic medium, to solve problems involving the high-speed introduction of the rigid solids into a continuum. Particular interest concerns the application of the mathematical approaches developed for the analysis of multilayered armor and the study of thin-walled structural elements in civil and mechanical engineering. The study of the influence of thin inhomogeneities on the stress/strain state of solids is a natural extension of the consecutive development of the above-mentioned range of problems. At present, there are two basic approaches to the theoretical study of solids containing thin inhomogeneities. The first one is a direct approach (3-5) in which an inclusion is considered as an object with a certain thickness. The second one is a special approach (6-9) which