In frameworks of simple mathematical model the nonlinear synthesis problem of a plane equidistant antenna array according to the given requirements to an amplitude directivity pattern is considered. When finding the branching curves of solutions of nonlinear integral equations, obtained as a result of solution of the synthesis problem, the two-parameter eigenvalue problems with spectral parameters analytically included in the kernel of the linearized integral operator arise. For such problems the numerical algorithm of finding the eigenvalue curves are considered. The numerical examples are presented.