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One approach to the numerical solution of synthesis problem of antennas with flat radiating aperture according to the prescribed requirements to amplitude directivity pattern and presence of restrictions on norm of currents of excitation is stated. Nonuniqueness and branching of the solutions are characteristics of such class of problems. Finding the optimum solutions is reduced to investigation and numerical solution of Hammestein type nonlinear two-dimensional integral equation. Numerical algorithms for finding the branching lines and branch off solutions of this equation are constructed and justified. Numerical examples are given.