A theoretical approach for describing the electromagnetic radiation produced by a prolonged electron bunch propagating in the lattice of metallic wires of finite length is presented. This approach is based on the vibrator antenna theory and involves the approximate solving of Hallen's integral equation. For a single wire, it is also supposed that a wire is sufficiently thin and charge motion is relativistic. For many-wire structures, the approximation similar to the kinematic approach of the parametric x-ray radiation theory is additionally applied. The validity of the method is verified by numerical simulations with comsoL Multiphysics. Possible applications of the interaction between charged particle bunches and artificial wire structures arc discussed.