Abstract:Background. The paper is devoted to the one of the urgent problem - the synthesis problem of anisotropic multilayer coating. The purpose of the study is to develop a numerical-analytical method for solving of the synthesis problem of anisotropic multilayer coatings. Materials and methods. The problem of the synthesis of anisotropic multilayer coating is investigated: the problem is reduced to solving an optimization problem. Results. The developed algorithms for solving the problem can be used in the synthesis of multilayer anisotropic coatings. Conclusions. The numerical methods of solving these inverse problems and numerical results can be used in practice to reconstruct electromagnetic characteristics of modern materials.