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This paper presents a numerical and experimental verification of an approximate but efficient integral equation technique for the scattering by apertures in conducting planes with finite thicknesses. The approach is based on a perturbation method and modified Green's functions that take into account the finite metallization thickness. The computational effort and time needed for solving the problem are the same as in zero-thickness case. When compared to full-wave cavity treatment of thick apertures, the method is (depending on the number of unknowns) at least an order of magnitude faster. The method can be applied even to apertures of arbitrary shapes where computing the cavity's Green's functions is a difficult task. The results of simulations using the new approach show good agreement when compared to both results from full-wave cavity approach and measurements.