The results of investigations of synthesis antennas problems with a flat radiating aperture according to the prescribed amplitude directivity pattern (DP) in the different variational formulations are presented. The non-uniqueness and branching of solutions are characteristic for problems of this class. The methods for finding the branching lines of solutions dependent on the sizes of the aperture and properties of the prescribed amplitude DP are stated; justified algorithms for finding the optimal solutions of synthesis problem are presented. It is shown that finding the optimal phase DP improves significantly the quality of the approximation of synthesized DP to the prescribed in comparison with synthesis in the class of in-phase DP. In particular, it permits to decrease the sizes of antenna aperture at the same efficiency of synthesis in comparison to synthesis in the class in-phase DP nearly per 30%.