Boundary-value problems of scattering from finite number of circular apertures in conducting planes are solved rigorously. The scattered fields are represented in terms of discrete and continuous modes based on the eigen function expansion, integral transform, and superposition principle. The boundary conditions are enforced to obtain a set of simultaneous equations for discrete modal coefficients. The polarizabilities, transmission coefficients, and coupling parameters are expressed in rapidly convergent series. Computation is performed to illustrate the scattering behavior in terms of aperture geometry or frequency. Electromagnetic coupling through a flanged coaxial line array is studied. An approximate TEM mode solution is obtained by using the Hankel transform and superposition principle and compared with the measured data. We also solve the problem rigorously by considering higer-order modes and compare with the approximate solution. Our theoretical approach enables us to perform computation more efficiently than numerical techniques. Our method also allows us to solve the boundary-value problem dealing with scattering from fininte number of different-sized circular apertures arbitrarily located on conducting planes while floquet`s theorem is applicable to only periodic structures. Our results are expected to find practical applications in frequency selective surface (FSS), aperture array antennas, and EMI/EMC problems.