Pattern in all planes of observation in the front half, gain, efficiency antenna area, the width of the main lobe, the levels of lateral and cross-polarized radiation axially symmetric parabolic reflector antennas are designed by method of currents the physical theory of diffraction. The irradiator is given in the form of the approximate mathematical model within the aperture theory. Shading reflector focal unit in the algorithm and computer programs recorded. It is shown that the system is a "reflector + irradiator" can be optimized for maximum gain when a predetermined maximum level sidelobes. Influence of the size of a parabolic reflector (in the calculation of the diameter varied from 10 to 100 wavelengths) and its focal length (focal length to the diameter of the reflector was varied from 0.5 to 3.0) studied in detail. It is shown that in the case of antennas optimized maximum level and cross-polarized radiation is weakly dependent on the diameter of the reflector and decreases with increasing depth of the reflector.