Printed multilayered media with metallizations embedded between dielectric layers are one of the most successful technologies for manufacturing planar structures with a good performanceto-price ratio. These structures range from PC board circuits, through cavity backed antennas and antenna arrays used in satellite communications, to waveguide filters. The approach most commonly used to model and analyze the aforementioned structures is the Integral Equation (IE) technique solved with Method of Moments (MoM). Applying IE-MoM with subsectional basis functions to electromagnetically large structures is demanding in terms of both computer memory allocation and time needed to solve the problem. Computationally efficient techniques are thus needed to accelerate the IE-MoM procedures and allow modeling of large circuits and antennas on standard desktop PCs. Subdomain Multilevel Approach (SMA) with Macro-Basis Functions (MBF) is one of the acceleration techniques, developed in our laboratory. Its application to modeling large antenna arrays has already proven to be very efficient. However, this technique can be improved, especially when MoM matrix filling time is concerned. This thesis proposes an improvement of the SMA using equivalent moments in computing the interactions between macro-basis functions. It shows that, without significant loss of accuracy, we obtain a two-fold gain in computational time for structures with the number of unknowns of the order 104. In structures operating at higher frequencies (thin films in millimeter and submillimeter wave bands) or with self supporting metallic plates, the thickness of metallic screens must be taken into account. Multilayered structures with apertures (holes) in thick conducting screens can be accurately modeled using the equivalence theorem and magnetic currents introduced at both aperture interfaces. This approach, however, doubles the number of unknowns as compared to that one of the zero-thickness case. Moreover, the thick aperture problem asks for the computation of cavity Green's functions, which is a difficult and time-consuming task for apertures of arbitrary cross-sections. This thesis addresses the problem of scattering by apertures in thick conducting screens by introducing an approximate and computationally efficient formulation. This formulation consists in treating the thick aperture as an infinitely thin one and in using the correction term in integral equation kernel that accounts for the screen thickness. The number of unknowns remains the same as in the zero-thickness screens and evaluation of complicated cavity Green's functions is obviated, which yields computationally efficient routines. The technique is successfully applied to self-supporting aperture antennas and thick irises within multilayered rectangular waveguides giving good results for apertures whose thickness is smaller than their lateral dimensions.