The analysis of a multilayered structure consisting of several planar spiral conductors with a common vertical axis is reduced to a treatment of certain rotationally symmetric electro- and magnetostatic field problems. These problems are solved using the variational method and the Rayleigh-Ritz procedure. The unknown charge and current distributions on the surfaces of the conductors are estimated by compact sets of basis functions. Due to the inhomogeneity of the medium the treatment is carried out in the Hankel-transformed domain. The elements of the resulting capacitance and inductance matrices are used to create a network model for the original structure. Finally, the method is verified against FEM simulations in a case of a simple spiral inductor, and a good agreement is found.