In this paper, the problem of electromagnetic transmission through slits in two parallel conducting plates which separate two half spaces is considered. The coupled integral equations for the electric field distributions over the slits are developed for the case that the TM polarized plane wave is incident on the slit and solved by the method of moments. The transmitted power beyond the slit-perforated conducting parallel plates is computed in order to check the variations of the coupled power through slits against some parameters such as the incident angle of the TM polarized wave, slit width, lateral distance between two slits, and distance between the conducting plates. When the lateral distance between two slits approaches near the multiples of half wavelengths, the transmission resonance (maximum power transmission) is observed. If the slit width in the incident side is narrow and the distance between conducting plates is small compared to the wavelength, the maximum of transmitted power is observed to be nearly independent of the incident angle and slit width. In addition, the mechanism of the transmission resonance in the present geometry is explained using a simplified geometry and its equivalent circuit.