The radiation from parabolic reflector antennas for different amplitude and phase aperture illumination patterns is treated and the minimizations of the edge diffraction effects by edge rolling techniques are investigated in ail accurate manner. The analytical regularization method (ARM) is used to solve the problem of E-polarized wave diffraction by parabolic shaped perfectly electrical conductive (PEC) cylindrical reflector with finite thickness. The initial boundary value problem is reduced to the infinite algebraic system of the second kind, which is ail equation that call in principal be solved with any predetermined accuracy by means of the truncation procedure. The parabolic reflector is illuminated by a fictive feeder antenna which produces the desired phase and amplitude field distributions over the antenna aperture. Some edge rolling structures are analyzed to suppress the side and back lobes and to improve the aperture efficiency. The ARM procedure is verified by the analytical solutions and the calculated field patterns are presented for typical antenna configurations. (c) 2005 Elsevier GmbH. All rights reserved.