A spectral domain analysis is presented of a plane wave-excited subwavelength circular aperture in a planar perfectly conducting screen in close proximity to a multilayer stack, which may comprise uniaxially anisotropic slices. The formulation employs the Bethe-Bouwkamp aperture model for the general case of oblique incidence, and it combines the Hankel transform method with a transmission line network analogue of the medium, which facilitates the inclusion of any number of material layers. The electromagnetic fields are expressed in terms of one-dimensional (1-D) Hankel transform integrals, which are efficiently evaluated by a numerical quadrature along a suitably selected path, with convergence acceleration by extrapolation. Sample numerical results are presented to demonstrate the validity of the method and its utility in the modeling of multilayer near-field lenses and aperture-type probes of near-field optical microscopy.