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We present a theoretical and numerical framework to analyze optical properties of subwavelength apertures that are distributed arbitrarily on the 2-D plane of a metal film. Using the radiation patterns linked to individual eigenmodes inside the aperture, the coupling between multiple apertures is described efficiently by a small-rank linear system of equations. The complicated contributions from both the surface plasmon polariton (SPP) and creeping wave are inherently included in the analysis. Three-dimensional fully vectorial finite-difference time-domain calculations are used to verify the model in several test cases. The model accurately predicts all the salient features in extraordinary optical transmission (EOT) spectra of 2-D nanoslit arrays, including the surface plasmon resonances and Rayleigh-Wood anomalies. We also explore the effects of finite array size on EOT and discover a novel regime where the EOT efficiency decreases with an increasing number of apertures. Finally, we apply the model in calculating SPP excitation by an arbitrarily patterned nanoslit array. The presented method not only provides deeper physical insights into EOT and related phenomena, but should also be useful in designing a variety of novel aperiodic plasmonic devices with drastically less computational cost.