Abstract <p>The problem of constructing approximation models for radiating and reradiating structures that make it possible to reconstruct the distribution of sources of the radiated and scattered electromagnetic fields with a known accuracy without a rigorous solution to the corresponding electrodynamic problem is considered. As a basis for constructing approximation models it is proposed to use the eigenfunction method, in which the distribution of sources and third-party electromagnetic fields on the surface and (or) in the volume of the structures under consideration are represented as an eigenfunction expansion of the corresponding integral operator, and the expansion coefficients are determined by its eigenvalues and the type of function of the external electromagnetic field. It is shown that the problem considered has many possible solutions. Techniques for the development of approximation models, as well as a methodology for assessing errors introduced at various stages of development are proposed. As an example, one of the possible options for constructing an approximation model for a tubular dipole is given. The results of numerical simulations are presented.</p>