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In many cases, the effectiveness of an electromagnetic shield is determined by apertures that exist in the shield. To minimize the penetration of EM fields through a large aperture, the aperture is sometimes loaded with conductive material. The solution of the loaded aperture problem can be reduced to the calculation of equivalent magnetic surface currents, [right arrow [M.sub.s]], that exist over the surface of the aperture. In this paper, the relevant integro-differential equations have been solved using the Method of Moments to determine [right arrow [M.sub.s]] for a small, square aperture loaded with a number of impedance sheets of practical interest. These values of [right arrow [M.sub.s]] have been used to calculate the magnetic and electric insertion losses of these impedance sheets. The numerical results are compared with shielding measurements we have made on carbon composite materials and wire meshes and grids.