A comparison of three methods of solution for the problem of scattering and diffraction of a transverse electric (TE) polarized plane wave by an infinite circular cylinder having an infinite axial slot is presented. In one method of solution, the aperture field integral equation (AFIE) method, the fields in and around the cylinder are found from the apertureE-field and the Green's functions for the interior and exterior of a cylinder. In the other two methods, the fields are determined from the surface current, which is obtained by solution of theH-field integral equation (HFIE) or theE-field integral equation (EFIE). The field in the aperture of the cylinder is found from the three methods, and the advantages and disadvantages of each method of solution are discussed. In addition, it is also shown that for shell thickness less than 1/20 of a wavelength, the aperture fields do not differ signifcantly from those of an infinitely thin shell cylinder.