The electromagnetic field transmitted by a subwavelength circular aperture in a perfectly conducting screen of infinitesimal thickness and illuminated by an obliquely incident plane wave is analyzed based on the Bethe-Bouwkamp quasi-static model of the field in the aperture plane. The problem is formulated in the spectral domain and the solution is expressed in terms of a minimum number of one-dimensional Hankel-transform integrals involving products of Bessel functions and spherical Bessel functions. An efficient computational scheme for these integrals is implemented, based on numerical quadrature with convergence acceleration by extrapolation. From the rigorous spectral domain formulation, closed form expressions are also derived for the transmitted near-zone and far-zone fields. Sample numerical results are presented to demonstrate the validity of the method and its utility in the modeling of aperture-type near-field optical probes.