Electromagnetic power transmission through two cyl-inder-penetrated circular apertures in parallel conducting planes is studied. The Weber transform and superposition principle are used to represent the scattered field. A set of simultaneous equations for the modal coefficients are constituted based on the mode-matching and boundary conditions. The whole integration path is slightly deformed into a new one below the positive real axis not to pass through the pole singularities encountered on the original path so that it is easily calculated by direct numerical quadrature. Computation shows the behaviors of power transmission in terms of aperture geometry and wavelength. The presented scheme is very amenable to numerical evaluations and useful for various electromagnetic scattering and antenna radiation analysis involved with singularity problems.