This paper focuses on the shielding effectiveness estimation of the periodic circular aperture array on a lossy infinite plane against a plane electromagnetic wave, while its wavelength is much larger than the central distance of the aperture. The circuit model and the analytical expression are proposed based on calculation for the conductor plane with periodic circular apertures and the lossy plane. The circuit model of the lossy plane with apertures is obtained by connecting the circuit of the lossy plane, which is obtained by the equivalent of the two-port network, in series with the equivalent impedance of the conductor plane with apertures. The expression of the lossy plane with apertures is obtained by doing some mathematical operation on expressions of lossy plane and conductor plane with apertures. Results shows that both the circuit model and the expression are in good agreement compared with the full-wave simulation.