Analytical methods are significantly useful tools for engineers in computational modeling. These methods provide fast simulations, while preserving physical meaning. In this paper, a full analytical formulation is developed based on the circuit approach, also known as Intermediate Level Circuit Model (ILCM), to evaluate the shielding effectiveness (SE) of metallic structures. The proposal focuses on rectangular enclosures containing apertures of complex geometrical shape, illuminated by an external plane wave. The enclosure is taken as a short-circuited waveguide. The aperture is treated as a transmission line with an intrinsic impedance that depends on the aperture polarizability, according to Bethe's theory of small holes. The formulation easily takes into account high-order resonant modes and different apertures, such as circular, elliptical, round-ended and cross-shaped apertures. The ILCM technique reveals good agreement with a numerical full-wave method for various configurations of enclosures, covering a large range of frequencies from 0.5 GHz to 2.5 GHz, thus offering perspectives for parametric and/or optimization SE studies.